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Instant-use add-on functions for the Wolfram Language
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Replace all occurrences of an algebraic subexpression with a new symbol
ResourceFunction["AlgebraicReplace"][expr,reps,repvars] rewrites expr, replacing each occurrence of an element of reps with the corresponding element of repvars. | |
ResourceFunction["AlgebraicReplace"][expr,reps,repvars,vars] rewrites expr, burrowing inside any subexpression that is not a polynomial in vars. |
Algebraically replace xy by a new variable z in a bivariate polynomial:
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AlgebraicReplace works with non-polynomial expressions:
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Use several replacements at once:
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ReplaceAll only replaces literal matches:
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AlgebraicReplace rewrites all monomials containing powers of xy to have powers of z:
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AlgebraicReplace with a set of reducing polynomials polys and replacement variables vars has behavior similar to PolynomialReduce with polys-vars:
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This is not canonical insofar as the reduction is not done with a Gröbner basis, so results can depend on ordering of inputs:
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If we compute a Gröbner basis then the result is canonical for the given variable ordering:
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Reversing the reduction polynomials does not change the result of PolynomialReduce when a Gröbner basis is used:
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If the underlying variables are omitted, AlgebraicReplace might not recognize what are the correct ones:
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Specify x and y as variables to get the desired replacement:
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As seen in the "Properties and Relations" examples, AlgebraicReplace does not compute and use a Gröbner basis. Changing the order of the reducer inputs can affect the result.
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