{"id":479217,"date":"2023-08-09T10:31:59","date_gmt":"2023-08-09T10:31:59","guid":{"rendered":""},"modified":"2023-09-05T11:18:23","modified_gmt":"2023-09-05T11:18:23","slug":"symbolic-computation","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/ar\/wiki\/symbolic-computation\/","title":{"rendered":"\u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a"},"content":{"rendered":"<p>\u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a\u060c \u0627\u0644\u0645\u0639\u0631\u0648\u0641 \u0623\u064a\u0636\u064b\u0627 \u0628\u0627\u0633\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u0631\u0645\u0632\u064a\u0629 \u0623\u0648 \u062c\u0628\u0631 \u0627\u0644\u0643\u0645\u0628\u064a\u0648\u062a\u0631\u060c \u0647\u0648 \u0641\u0631\u0639 \u0645\u0646 \u0639\u0644\u0648\u0645 \u0627\u0644\u0643\u0645\u0628\u064a\u0648\u062a\u0631 \u0648\u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a 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\u0627\u0644\u0623\u062f\u0644\u0629.<\/p>\n<\/li>\n<\/ol>\n<h2>\u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a<\/h2>\n<p>\u064a\u0634\u0645\u0644 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u062d\u0642\u0648\u0644 \u0627\u0644\u0641\u0631\u0639\u064a\u0629 \u0648\u0627\u0644\u0623\u062f\u0648\u0627\u062a\u060c \u0643\u0644 \u0645\u0646\u0647\u0627 \u064a\u062e\u062f\u0645 \u0645\u0647\u0627\u0645 \u0631\u064a\u0627\u0636\u064a\u0629 \u0645\u062d\u062f\u062f\u0629. \u062a\u0634\u0645\u0644 \u0627\u0644\u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629 \u0644\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a \u0645\u0627 \u064a\u0644\u064a:<\/p>\n<table>\n<thead>\n<tr>\n<th>\u064a\u0643\u062a\u0628<\/th>\n<th>\u0648\u0635\u0641<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a\u0629 (CAS)<\/td>\n<td>\u0628\u0631\u0646\u0627\u0645\u062c \u0634\u0627\u0645\u0644 \u064a\u0642\u0648\u0645 \u0628\u0625\u062c\u0631\u0627\u0621 \u062d\u0633\u0627\u0628\u0627\u062a \u0631\u0645\u0632\u064a\u0629\u060c \u0628\u062f\u0621\u064b\u0627 \u0645\u0646 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u062c\u0628\u0631\u064a\u0629 \u0648\u062d\u062a\u0649 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0627\u0644\u0645\u062a\u0642\u062f\u0645\u0629. \u062a\u0634\u0645\u0644 CAS \u0627\u0644\u0634\u0627\u0626\u0639\u0629 Mathematica \u0648Maple \u0648Maxima.<\/td>\n<\/tr>\n<tr>\n<td>\u0645\u0643\u062a\u0628\u0627\u062a \u0627\u0644\u062a\u0644\u0627\u0639\u0628 \u0627\u0644\u0631\u0645\u0632\u064a<\/td>\n<td>\u0627\u0644\u0645\u0643\u062a\u0628\u0627\u062a \u0623\u0648 \u0627\u0644\u0648\u062d\u062f\u0627\u062a \u0627\u0644\u0645\u062f\u0645\u062c\u0629 \u0641\u064a \u0644\u063a\u0627\u062a \u0627\u0644\u0628\u0631\u0645\u062c\u0629 (\u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c SymPy for Python) \u0627\u0644\u062a\u064a \u062a\u0645\u0643\u0646 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u064a\u0646 \u0645\u0646 \u0625\u062c\u0631\u0627\u0621 \u062d\u0633\u0627\u0628\u0627\u062a \u0631\u0645\u0632\u064a\u0629 \u0645\u0628\u0627\u0634\u0631\u0629 \u062f\u0627\u062e\u0644 \u0627\u0644\u062a\u0639\u0644\u064a\u0645\u0627\u062a \u0627\u0644\u0628\u0631\u0645\u062c\u064a\u0629 \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0647\u0645.<\/td>\n<\/tr>\n<tr>\n<td>\u0645\u062b\u0628\u062a\u0627\u062a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0643\u0645\u0628\u064a\u0648\u062a\u0631<\/td>\n<td>\u0623\u062f\u0648\u0627\u062a \u0645\u0635\u0645\u0645\u0629 \u0644\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0627\u0644\u0631\u0633\u0645\u064a\u060c \u0645\u0645\u0627 \u064a\u0633\u0645\u062d \u0628\u0627\u0644\u0623\u062f\u0644\u0629 \u0627\u0644\u0622\u0644\u064a\u0629 \u0648\u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u0627\u0644\u0646\u0638\u0631\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629. \u0648\u0645\u0646 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0630\u0644\u0643 HOL Light \u0648Isabelle.<\/td>\n<\/tr>\n<tr>\n<td>\u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0647\u062c\u064a\u0646\u0629 \u0627\u0644\u0631\u0645\u0632\u064a\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629<\/td>\n<td>\u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u062a\u064a \u062a\u062c\u0645\u0639 \u0628\u064a\u0646 \u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u0631\u0645\u0632\u064a\u0629 \u0648\u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0644\u0644\u0627\u0633\u062a\u0641\u0627\u062f\u0629 \u0645\u0646 \u0645\u0632\u0627\u064a\u0627 \u0643\u0644 \u0646\u0647\u062c\u060c \u0648\u062a\u062d\u0642\u064a\u0642 \u062d\u0633\u0627\u0628\u0627\u062a \u0623\u0643\u062b\u0631 \u0643\u0641\u0627\u0621\u0629.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u0637\u0631\u0642 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a \u0648\u0645\u0634\u0643\u0644\u0627\u062a\u0647 \u0648\u062d\u0644\u0648\u0644\u0647\u0627 \u0627\u0644\u0645\u062a\u0639\u0644\u0642\u0629 \u0628\u0627\u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645<\/h2>\n<p>\u064a\u062c\u062f \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a \u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0641\u064a \u0645\u062c\u0627\u0644\u0627\u062a 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\u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a.<\/p>\n<\/li>\n<li>\n<p><strong>\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0648\u0627\u0644\u0647\u0646\u062f\u0633\u0629<\/strong>: \u064a\u0633\u0627\u0639\u062f \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a \u0641\u064a \u062d\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0626\u064a\u0629 \u0627\u0644\u0645\u0639\u0642\u062f\u0629 \u0648\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0648\u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u0646\u0645\u0630\u062c\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0641\u064a \u0627\u0644\u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629.<\/p>\n<\/li>\n<li>\n<p><strong>\u062a\u0639\u0644\u064a\u0645<\/strong>: \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a \u0647\u0648 \u0623\u062f\u0627\u0629 \u062a\u0639\u0644\u064a\u0645\u064a\u0629 \u0642\u064a\u0645\u0629 \u0644\u062a\u062f\u0631\u064a\u0633 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a\u060c \u062d\u064a\u062b \u064a\u0645\u0643\u0646\u0647 \u0639\u0631\u0636 \u0627\u0644\u062d\u0644\u0648\u0644 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0648\u062a\u0635\u0648\u0631 \u0627\u0644\u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0645\u062c\u0631\u062f\u0629.<\/p>\n<\/li>\n<li>\n<p><strong>\u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644 \u0627\u0644\u0622\u0644\u064a<\/strong>: \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a \u0641\u064a \u0623\u0628\u062d\u0627\u062b \u0627\u0644\u0630\u0643\u0627\u0621 \u0627\u0644\u0627\u0635\u0637\u0646\u0627\u0639\u064a \u0644\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644 \u0627\u0644\u0622\u0644\u064a \u0648\u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644 \u0627\u0644\u0645\u0646\u0637\u0642\u064a \u0648\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0645\u0639\u0631\u0641\u0629.<\/p>\n<\/li>\n<li>\n<p><strong>\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0634\u0641\u0631\u0627\u062a<\/strong>: \u064a\u0644\u0639\u0628 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a \u062f\u0648\u0631\u064b\u0627 \u0641\u064a \u0647\u062c\u0645\u0627\u062a \u0627\u0644\u062a\u0634\u0641\u064a\u0631 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0633\u062a\u0643\u0634\u0627\u0641 \u0646\u0642\u0627\u0637 \u0627\u0644\u0636\u0639\u0641 \u0648\u0625\u064a\u062c\u0627\u062f \u0646\u0642\u0627\u0637 \u0627\u0644\u0636\u0639\u0641 \u0641\u064a \u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u062a\u0634\u0641\u064a\u0631.<\/p>\n<\/li>\n<li>\n<p><strong>\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u062a\u062d\u0643\u0645<\/strong>: \u0641\u064a \u0647\u0646\u062f\u0633\u0629 \u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u062a\u062d\u0643\u0645\u060c \u064a\u0633\u0627\u0639\u062f \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0627\u0633\u062a\u0642\u0631\u0627\u0631 \u0648\u0625\u0645\u0643\u0627\u0646\u064a\u0629 \u0627\u0644\u062a\u062d\u0643\u0645 \u0648\u0625\u0645\u0643\u0627\u0646\u064a\u0629 \u0645\u0644\u0627\u062d\u0638\u0629 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u064a\u0629.<\/p>\n<\/li>\n<li>\n<p><strong>\u0627\u0644\u062a\u0635\u0645\u064a\u0645 \u0628\u0645\u0633\u0627\u0639\u062f\u0629 \u0627\u0644\u062d\u0627\u0633\u0648\u0628<\/strong>: \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a \u064a\u0633\u0647\u0644 \u0627\u0644\u0646\u0645\u0630\u062c\u0629 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629 \u0648\u0627\u0644\u062a\u0635\u0645\u064a\u0645 \u0627\u0644\u0628\u0627\u0631\u0627\u0645\u062a\u0631\u064a \u0641\u064a \u0628\u0631\u0627\u0645\u062c \u0627\u0644\u062a\u0635\u0645\u064a\u0645 \u0628\u0645\u0633\u0627\u0639\u062f\u0629 \u0627\u0644\u0643\u0645\u0628\u064a\u0648\u062a\u0631 (CAD).<\/p>\n<\/li>\n<\/ol>\n<p><strong>\u0627\u0644\u062a\u062d\u062f\u064a\u0627\u062a \u0648\u0627\u0644\u062d\u0644\u0648\u0644 \u0627\u0644\u0645\u0634\u062a\u0631\u0643\u0629:<\/strong><\/p>\n<ol>\n<li>\n<p><strong>\u062a\u0639\u0642\u064a\u062f \u0627\u0644\u062a\u0639\u0628\u064a\u0631<\/strong>: \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0624\u062f\u064a \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0627\u0644\u062a\u0639\u0628\u064a\u0631\u0627\u062a \u0627\u0644\u0643\u0628\u064a\u0631\u0629 \u0623\u0648 \u0627\u0644\u0645\u0639\u0642\u062f\u0629 \u0644\u0644\u063a\u0627\u064a\u0629 \u0625\u0644\u0649 \u062d\u062f\u0648\u062b \u0645\u0634\u0643\u0644\u0627\u062a \u0641\u064a \u0627\u0644\u0623\u062f\u0627\u0621. \u0625\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0645\u062d\u0633\u0646\u0629 \u0648\u0627\u0644\u062d\u0648\u0633\u0628\u0629 \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u0629 \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u062e\u0641\u0641 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0645\u0634\u0627\u0643\u0644.<\/p>\n<\/li>\n<li>\n<p><strong>\u0639\u062f\u0645 \u0627\u0644\u0627\u0633\u062a\u0642\u0631\u0627\u0631 \u0627\u0644\u0639\u062f\u062f\u064a<\/strong>: \u0642\u062f \u064a\u0648\u0627\u062c\u0647 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a \u0639\u062f\u0645 \u0627\u0633\u062a\u0642\u0631\u0627\u0631 \u0631\u0642\u0645\u064a \u0639\u0646\u062f \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0627\u0644\u0648\u0638\u0627\u0626\u0641 \u0630\u0627\u062a \u0627\u0644\u062a\u0641\u0631\u062f\u0627\u062a \u0623\u0648 \u0627\u0644\u0646\u0642\u0627\u0637 \u063a\u064a\u0631 \u0627\u0644\u0645\u062d\u062f\u062f\u0629. \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0624\u062f\u064a \u062f\u0645\u062c \u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0644\u062d\u0627\u0644\u0627\u062a \u0645\u062d\u062f\u062f\u0629 \u0625\u0644\u0649 \u062d\u0644 \u0645\u062b\u0644 \u0647\u0630\u0647 \u0627\u0644\u0645\u0634\u0643\u0644\u0627\u062a.<\/p>\n<\/li>\n<li>\n<p><strong>\u062d\u062f\u0648\u062f \u0627\u0644\u062d\u0644\u0648\u0644 \u0627\u0644\u062f\u0642\u064a\u0642\u0629<\/strong>: \u0628\u0639\u0636 \u0627\u0644\u0645\u0634\u0627\u0643\u0644 \u0644\u064a\u0633 \u0644\u0647\u0627 \u062d\u0644\u0648\u0644 \u0631\u0645\u0632\u064a\u0629 \u0645\u063a\u0644\u0642\u0629. \u0641\u064a \u0645\u062b\u0644 \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0627\u062a\u060c \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0642\u0631\u064a\u0628\u0627\u062a \u0627\u0644\u0631\u0642\u0645\u064a\u0629 \u0623\u0648 \u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u0631\u0642\u0645\u064a\u0629 \u0627\u0644\u0631\u0645\u0632\u064a\u0629 \u0627\u0644\u0647\u062c\u064a\u0646\u0629.<\/p>\n<\/li>\n<li>\n<p><strong>\u0627\u0644\u062a\u0628\u0633\u064a\u0637 \u0627\u0644\u0631\u0645\u0632\u064a<\/strong>: \u0636\u0645\u0627\u0646 \u0627\u0644\u062a\u0628\u0633\u064a\u0637 \u0627\u0644\u0641\u0639\u0627\u0644 \u0648\u0627\u0644\u0635\u062d\u064a\u062d \u0644\u0644\u062a\u0639\u0628\u064a\u0631\u0627\u062a \u064a\u062a\u0637\u0644\u0628 \u0627\u0644\u062a\u062d\u0633\u064a\u0646 \u0627\u0644\u0645\u0633\u062a\u0645\u0631 \u0648\u062a\u062d\u0633\u064a\u0646 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062a\u0628\u0633\u064a\u0637.<\/p>\n<\/li>\n<\/ol>\n<h2>\u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629 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\u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u062c\u0628\u0631\u064a \u0648\u0627\u0644\u0645\u0646\u0637\u0642\u064a<\/td>\n<\/tr>\n<tr>\n<td>\u0645\u0641\u064a\u062f\u0629 \u0644\u062d\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0631\u0645\u0632\u064a\u0627<\/td>\n<\/tr>\n<tr>\n<td>\u0645\u0646\u0627\u0633\u0628\u0629 \u0644\u0644\u062a\u062d\u0642\u064a\u0642\u0627\u062a \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0648\u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<thead>\n<tr>\n<th>\u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a \u0645\u0642\u0627\u0628\u0644 \u0627\u0644\u062a\u062d\u0642\u0642 \u0627\u0644\u0631\u0633\u0645\u064a<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a<\/td>\n<\/tr>\n<tr>\n<td>\u064a\u0631\u0643\u0632 \u0639\u0644\u0649 \u0627\u0644\u062a\u0639\u0628\u064a\u0631\u0627\u062a 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\u0627\u0644\u0631\u0645\u0632\u064a \u0625\u0644\u0649 \u0625\u062d\u062f\u0627\u062b \u062b\u0648\u0631\u0629 \u0641\u064a \u0645\u062c\u0627\u0644\u0627\u062a \u0645\u062b\u0644 \u0627\u0644\u062a\u0634\u0641\u064a\u0631 \u0648\u0627\u0644\u062a\u062d\u0633\u064a\u0646\u060c \u0645\u0645\u0627 \u064a\u0648\u0641\u0631 \u0633\u0631\u0639\u0629 \u0647\u0627\u0626\u0644\u0629 \u0645\u0642\u0627\u0631\u0646\u0629 \u0628\u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629.<\/p>\n<\/li>\n<li>\n<p><strong>\u062a\u0643\u0627\u0645\u0644 \u0627\u0644\u062a\u0639\u0644\u0645 \u0627\u0644\u0622\u0644\u064a<\/strong>: \u064a\u0645\u0643\u0646 \u0644\u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u062a\u0639\u0644\u0645 \u0627\u0644\u0622\u0644\u064a \u062a\u0639\u0632\u064a\u0632 \u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u062d\u0633\u064a\u0646 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062a\u0628\u0633\u064a\u0637 \u0648\u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0622\u0644\u064a \u0648\u0627\u0644\u062a\u0639\u0631\u0641 \u0639\u0644\u0649 \u0627\u0644\u0623\u0646\u0645\u0627\u0637.<\/p>\n<\/li>\n<li>\n<p><strong>\u0627\u0644\u062d\u0648\u0633\u0628\u0629 \u0639\u0627\u0644\u064a\u0629 \u0627\u0644\u0623\u062f\u0627\u0621<\/strong>: \u0627\u0644\u062a\u0642\u062f\u0645 \u0641\u064a \u0627\u0644\u062d\u0648\u0633\u0628\u0629 \u0639\u0627\u0644\u064a\u0629 \u0627\u0644\u0623\u062f\u0627\u0621 \u0633\u064a\u0645\u0643\u0646 \u0645\u0646 \u0625\u062c\u0631\u0627\u0621 \u062d\u0633\u0627\u0628\u0627\u062a \u0631\u0645\u0632\u064a\u0629 \u0623\u0633\u0631\u0639 \u0648\u0623\u0643\u062b\u0631 \u0643\u0641\u0627\u0621\u0629\u060c \u0645\u0645\u0627 \u064a\u0633\u0645\u062d \u0628\u0625\u062c\u0631\u0627\u0621 \u0639\u0645\u0644\u064a\u0627\u062a \u0645\u062d\u0627\u0643\u0627\u0629 \u0641\u064a \u0627\u0644\u0648\u0642\u062a \u0627\u0644\u062d\u0642\u064a\u0642\u064a \u0648\u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0639\u0642\u062f.<\/p>\n<\/li>\n<li>\n<p><strong>\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u062a\u062e\u0635\u0635\u0627\u062a<\/strong>: \u0633\u0648\u0641 \u064a\u0633\u062a\u0645\u0631 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a \u0641\u064a \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0641\u064a \u0645\u062c\u0627\u0644\u0627\u062a \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u062a\u062e\u0635\u0635\u0627\u062a\u060c \u0645\u062b\u0644 \u0639\u0644\u0645 \u0627\u0644\u0623\u062d\u064a\u0627\u0621 \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u060c \u0648\u0627\u0644\u0639\u0644\u0648\u0645 \u0627\u0644\u0627\u062c\u062a\u0645\u0627\u0639\u064a\u0629\u060c \u0648\u0627\u0644\u0645\u0627\u0644\u064a\u0629.<\/p>\n<\/li>\n<li>\n<p><strong>\u0627\u0644\u0623\u0633\u0627\u0644\u064a\u0628 \u0627\u0644\u0647\u062c\u064a\u0646\u0629 \u0627\u0644\u0631\u0645\u0632\u064a\u0629 \u0648\u0627\u0644\u0631\u0642\u0645\u064a\u0629<\/strong>: \u0625\u0646 \u062a\u0637\u0648\u064a\u0631 \u0623\u0633\u0627\u0644\u064a\u0628 \u0647\u062c\u064a\u0646\u0629 \u0623\u0643\u062b\u0631 \u0641\u0639\u0627\u0644\u064a\u0629 \u062a\u062c\u0645\u0639 \u0628\u064a\u0646 \u0627\u0644\u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u0631\u0645\u0632\u064a\u0629 \u0648\u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0633\u0648\u0641 \u064a\u0639\u0627\u0644\u062c \u0627\u0644\u0642\u064a\u0648\u062f \u0627\u0644\u0645\u0641\u0631\u0648\u0636\u0629 \u0639\u0644\u0649 \u0643\u0644 \u0646\u0647\u062c\u060c \u0648\u064a\u0642\u062f\u0645 \u062d\u0644\u0648\u0644\u0627\u064b \u0623\u0643\u062b\u0631 \u0642\u0648\u0629.<\/p>\n<\/li>\n<\/ol>\n<h2>\u0643\u064a\u0641 \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062e\u0648\u0627\u062f\u0645 \u0627\u0644\u0648\u0643\u064a\u0644\u0629 \u0623\u0648 \u0631\u0628\u0637\u0647\u0627 \u0628\u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a<\/h2>\n<p>\u062a\u0644\u0639\u0628 \u0627\u0644\u062e\u0648\u0627\u062f\u0645 \u0627\u0644\u0648\u0643\u064a\u0644\u0629 \u062f\u0648\u0631\u064b\u0627 \u062d\u064a\u0648\u064a\u064b\u0627 \u0641\u064a \u062a\u0639\u0632\u064a\u0632 \u0623\u062f\u0627\u0621 \u0648\u0623\u0645\u0627\u0646 \u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a:<\/p>\n<ol>\n<li>\n<p><strong>\u062a\u062d\u0633\u064a\u0646 \u0627\u0644\u0623\u062f\u0627\u0621<\/strong>: \u064a\u0645\u0643\u0646 \u0644\u0644\u062e\u0648\u0627\u062f\u0645 \u0627\u0644\u0648\u0643\u064a\u0644\u0629 \u062a\u062e\u0632\u064a\u0646 \u0627\u0644\u062a\u0639\u0628\u064a\u0631\u0627\u062a \u0648\u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u0629 \u0628\u0634\u0643\u0644 \u0645\u062a\u0643\u0631\u0631\u060c \u0645\u0645\u0627 \u064a\u0642\u0644\u0644 \u0627\u0644\u0639\u0628\u0621 \u0627\u0644\u062d\u0633\u0627\u0628\u064a \u0639\u0644\u0649 \u0645\u062d\u0631\u0643\u0627\u062a \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a\u0629.<\/p>\n<\/li>\n<li>\n<p><strong>\u0625\u062f\u0627\u0631\u0629 \u0639\u0631\u0636 \u0627\u0644\u0646\u0637\u0627\u0642 \u0627\u0644\u062a\u0631\u062f\u062f\u064a<\/strong>: \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0639\u0645\u0644 \u0643\u0648\u0633\u064a\u0637 \u0628\u064a\u0646 \u0627\u0644\u0639\u0645\u0644\u0627\u0621 \u0648\u0627\u0644\u062e\u0648\u0627\u062f\u0645\u060c \u064a\u0645\u0643\u0646 \u0644\u0644\u062e\u0648\u0627\u062f\u0645 \u0627\u0644\u0648\u0643\u064a\u0644\u0629 \u062a\u062d\u0633\u064a\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0646\u0637\u0627\u0642 \u0627\u0644\u062a\u0631\u062f\u062f\u064a \u0623\u062b\u0646\u0627\u0621 \u0645\u0647\u0627\u0645 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a\u060c \u062e\u0627\u0635\u0629 \u0639\u0646\u062f \u0627\u0644\u062a\u0641\u0627\u0639\u0644 \u0645\u0639 \u0645\u0648\u0627\u0631\u062f \u0627\u0644\u062d\u0633\u0627\u0628 \u0639\u0646 \u0628\u0639\u062f.<\/p>\n<\/li>\n<li>\n<p><strong>\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u062d\u0645\u0644<\/strong>: \u064a\u0645\u0643\u0646 \u0644\u0644\u062e\u0648\u0627\u062f\u0645 \u0627\u0644\u0648\u0643\u064a\u0644\u0629 \u062a\u0648\u0632\u064a\u0639 \u0637\u0644\u0628\u0627\u062a \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0648\u0627\u0631\u062f\u0629 \u0639\u0628\u0631 \u062e\u0648\u0627\u062f\u0645 \u0645\u062a\u0639\u062f\u062f\u0629\u060c \u0645\u0645\u0627 \u064a\u0636\u0645\u0646 \u0627\u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0641\u0639\u0627\u0644 \u0644\u0644\u0645\u0648\u0627\u0631\u062f \u0648\u0627\u0633\u062a\u062c\u0627\u0628\u0629 \u0623\u0641\u0636\u0644.<\/p>\n<\/li>\n<li>\n<p><strong>\u0627\u0644\u0623\u0645\u0646 \u0648\u0639\u062f\u0645 \u0627\u0644\u0643\u0634\u0641 \u0639\u0646 \u0647\u0648\u064a\u062a\u0647<\/strong>: \u062a\u0648\u0641\u0631 \u0627\u0644\u062e\u0648\u0627\u062f\u0645 \u0627\u0644\u0648\u0643\u064a\u0644\u0629 \u0637\u0628\u0642\u0629 \u0625\u0636\u0627\u0641\u064a\u0629 \u0645\u0646 \u0627\u0644\u0623\u0645\u0627\u0646\u060c \u0648\u062a\u062d\u0645\u064a \u0647\u0648\u064a\u0629 \u0648\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u064a\u0646 \u0627\u0644\u0645\u0634\u0627\u0631\u0643\u064a\u0646 \u0641\u064a \u0645\u0647\u0627\u0645 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a\u0629.<\/p>\n<\/li>\n<li>\n<p><strong>\u0635\u0644\u0627\u062d\u064a\u0629 \u0627\u0644\u062a\u062d\u0643\u0645 \u0635\u0644\u0627\u062d\u064a\u0629 \u0627\u0644\u062f\u062e\u0648\u0644<\/strong>: \u064a\u0645\u0643\u0646 \u0644\u0644\u062e\u0648\u0627\u062f\u0645 \u0627\u0644\u0648\u0643\u064a\u0644\u0629 \u0627\u0644\u062a\u062d\u0643\u0645 \u0641\u064a \u0627\u0644\u0648\u0635\u0648\u0644 \u0625\u0644\u0649 \u0645\u0648\u0627\u0631\u062f \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a\u0629 \u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u0645\u0635\u0627\u062f\u0642\u0629 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u060c \u0645\u0645\u0627 \u064a\u0645\u0646\u0639 \u0627\u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u063a\u064a\u0631 \u0627\u0644\u0645\u0635\u0631\u062d \u0628\u0647 \u0644\u0644\u0623\u0635\u0648\u0644 \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0629 \u0627\u0644\u0642\u064a\u0645\u0629.<\/p>\n<\/li>\n<\/ol>\n<h2>\u0631\u0648\u0627\u0628\u0637 \u0630\u0627\u062a \u0639\u0644\u0627\u0642\u0629<\/h2>\n<p>\u0644\u0645\u0632\u064a\u062f \u0645\u0646 \u0627\u0644\u0645\u0639\u0644\u0648\u0645\u0627\u062a \u062d\u0648\u0644 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a\u060c \u0641\u0643\u0631 \u0641\u064a \u0627\u0633\u062a\u0643\u0634\u0627\u0641 \u0627\u0644\u0645\u0648\u0627\u0631\u062f \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<ol>\n<li><a href=\"https:\/\/mathworld.wolfram.com\/SymbolicComputation.html\" target=\"_new\" rel=\"noopener nofollow\">Wolfram MathWorld \u2013 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a<\/a><\/li>\n<li><a href=\"https:\/\/www.sympy.org\/\" target=\"_new\" rel=\"noopener nofollow\">\u0648\u062b\u0627\u0626\u0642 \u0633\u064a\u0645\u0628\u064a<\/a><\/li>\n<li><a href=\"https:\/\/isabelle.in.tum.de\/\" target=\"_new\" rel=\"noopener nofollow\">\u0625\u062b\u0628\u0627\u062a \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0641\u064a \u0625\u064a\u0632\u0627\u0628\u064a\u0644<\/a><\/li>\n<li><a href=\"https:\/\/www.cambridge.org\/9780521837219\" target=\"_new\" rel=\"noopener nofollow\">\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a\u0629: \u062f\u0644\u064a\u0644 \u0639\u0645\u0644\u064a<\/a><\/li>\n<li><a href=\"https:\/\/www.springer.com\/gp\/book\/9781441917221\" target=\"_new\" rel=\"noopener nofollow\">\u0645\u0642\u062f\u0645\u0629 \u0641\u064a \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a \u0644\u0645\u0627\u064a\u0643\u0644 \u062c. \u062f\u064a\u0646\u064a\u0646<\/a><\/li>\n<\/ol>\n<p>\u064a\u0633\u062a\u0645\u0631 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a \u0641\u064a \u0627\u0644\u062a\u0637\u0648\u0631 \u0648\u062a\u0634\u0643\u064a\u0644 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u062a\u064a \u0646\u062a\u0639\u0627\u0645\u0644 \u0628\u0647\u0627 \u0645\u0639 \u0627\u0644\u0645\u0634\u0643\u0644\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0627\u0644\u0645\u0639\u0642\u062f\u0629. \u0625\u0646 \u0642\u062f\u0631\u062a\u0647\u0627 \u0639\u0644\u0649 \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0628\u0634\u0643\u0644 \u0631\u0645\u0632\u064a \u0648\u062a\u0642\u062f\u064a\u0645 \u062d\u0644\u0648\u0644 \u062f\u0642\u064a\u0642\u0629 \u062a\u0645\u0643\u0646 \u0627\u0644\u0628\u0627\u062d\u062b\u064a\u0646 \u0648\u0627\u0644\u0645\u0647\u0646\u062f\u0633\u064a\u0646 \u0648\u0627\u0644\u0645\u0639\u0644\u0645\u064a\u0646 \u0645\u0646 \u0627\u0633\u062a\u0643\u0634\u0627\u0641 \u062d\u062f\u0648\u062f \u062c\u062f\u064a\u062f\u0629 \u0641\u064a \u0627\u0644\u0639\u0644\u0648\u0645 \u0648\u0627\u0644\u062a\u0643\u0646\u0648\u0644\u0648\u062c\u064a\u0627\u060c \u0645\u0645\u0627 \u064a\u0624\u062f\u064a \u0625\u0644\u0649 \u0627\u062e\u062a\u0631\u0627\u0642\u0627\u062a \u0648\u062a\u0642\u062f\u0645\u0627\u062a \u0645\u0628\u062a\u0643\u0631\u0629. \u0645\u0639 \u062a\u0642\u062f\u0645 \u0627\u0644\u062a\u0643\u0646\u0648\u0644\u0648\u062c\u064a\u0627\u060c \u064a\u0639\u062f \u0627\u0646\u062f\u0645\u0627\u062c \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a \u0645\u0639 \u0627\u0644\u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0627\u0634\u0626\u0629 \u0645\u062b\u0644 \u0627\u0644\u062d\u0648\u0633\u0628\u0629 \u0627\u0644\u0643\u0645\u0648\u0645\u064a\u0629 \u0648\u0627\u0644\u062a\u0639\u0644\u0645 \u0627\u0644\u0622\u0644\u064a \u0628\u0645\u0633\u062a\u0642\u0628\u0644 \u0645\u062b\u064a\u0631\u060c \u0648\u064a\u0641\u062a\u062d \u0645\u062c\u0627\u0644\u0627\u062a \u062c\u062f\u064a\u062f\u0629 \u0645\u0646 \u0627\u0644\u0645\u0639\u0631\u0641\u0629 \u0648\u0627\u0644\u0627\u0643\u062a\u0634\u0627\u0641.<\/p>","protected":false},"featured_media":470631,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-479217","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about <mark>Symbolic Computation: Unleashing the Power of Mathematics<\/mark>","faq_items":[{"question":"What is Symbolic computation?","answer":"<p>Symbolic computation, also known as computer algebra, is a branch of computer science and mathematics that deals with manipulating mathematical expressions and symbols instead of numerical values. It enables computers to perform complex algebraic computations and mathematical operations symbolically, providing exact solutions.<\/p>"},{"question":"How did Symbolic computation originate?","answer":"<p>The roots of Symbolic computation can be traced back to the early 19th century, but it gained significant attention with the development of digital computers in the mid-20th century. One of the first notable mentions was the \"General Problem Solver\" (GPS) in 1960, which laid the foundation for further advancements in the field.<\/p>"},{"question":"What are the key features of Symbolic computation?","answer":"<p>Symbolic computation offers exact results, flexible handling of mathematical expressions, algorithmic manipulation, and the ability to perform logical reasoning and generalization. It is suitable for various applications, including mathematical research, physics, engineering, education, and automated reasoning.<\/p>"},{"question":"What types of Symbolic computation exist?","answer":"<p>Symbolic computation comes in various forms, including Computer Algebra Systems (CAS) like Mathematica and Maple, Symbolic Manipulation Libraries like SymPy for Python, Computer Theorem Provers, and Numerical Symbolic Hybrid Systems.<\/p>"},{"question":"How is Symbolic computation used, and what challenges does it face?","answer":"<p>Symbolic computation finds applications in mathematical research, physics simulations, education, artificial intelligence, and more. Challenges include handling expression complexity, numerical instabilities, limitations of exact solutions, and efficient simplification.<\/p>"},{"question":"How does Symbolic computation compare to Numerical Computation and Formal Verification?","answer":"<p>Symbolic computation deals with expressions and provides exact solutions, while numerical computation deals with numerical values and approximations. On the other hand, formal verification focuses on logical propositions and formal proofs.<\/p>"},{"question":"What is the future of Symbolic computation?","answer":"<p>The future of Symbolic computation looks promising with the integration of quantum computing, machine learning, and high-performance computing. It will continue to find applications in interdisciplinary fields and benefit from the development of hybrid symbolic-numeric approaches.<\/p>"},{"question":"How are proxy servers associated with Symbolic computation?","answer":"<p>Proxy servers optimize performance, manage bandwidth, and enhance security for Symbolic computation systems. They facilitate load balancing, access control, and provide an additional layer of anonymity during computational tasks.<\/p>"},{"question":"Where can I find more information about Symbolic computation?","answer":"<p>For more in-depth insights into Symbolic computation, check out the links provided in the \"Related links\" section, which include valuable resources, documentation, and books on the topic. Dive into the world of precise mathematics with OneProxy and explore the endless possibilities of Symbolic computation.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/wiki\/479217","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/wiki\/479217\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/media\/470631"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/media?parent=479217"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}