Inputing
simplify((( x^3+a*x+b) -(y^3+a*y+b) )^2/(x-y)^4)
ans =
(x^2 + x*y + y^2 + a)^2/(x - y)^2
feval(symengine,'Simplify',(( x^3+a*x+b) -(y^3+a*y+b) )^2/(x-y)^4,'OutputType = "Proof"')
get ans =
Input was \r\n (x^3 + a*x - y^3 - a*y)^2/(x - y)^4 \r\nApplying the rule\r\n () -> #X -> partfrac(#X, x, Mapcoeffs = proc(p)\r\n name polylib::sqrfree;\r\n local pp, pr, t, recollect, ret, options, unextend, ratsubsts, minpol, T, inds, Args, Float;\r\n begin\r\n pp := p; \r\n Args := [args()]; \r\n if nops(Args) = 2 && domtype(Args[2]) = DOM_BOOL then\r\n Args[2] := \"Recollect\" = Args[2]\r\n end_if; \r\n options := prog::getOptions(2, Args, faclib::defaultOptions, TRUE, faclib::optionTypes)[1]; \r\n recollect := (if options[\"Recollect\"] then\r\n proc(f)\r\n local t, i, j;\r\n begin\r\n t := table(); \r\n for i from 3 to nops(f) step 2 do\r\n if contains(t, f[i]) then\r\n t[f[i]] := t[f[i]]*f[i - 1]\r\n else \r\n t[f[i]] := f[i - 1]\r\n end_if\r\n end_for; \r\n [f[1], (op(t, [j, 2]), op(t, [j, 1])) $ j = 1..nops(t)]\r\n end_proc\r\n else \r\n id\r\n end_if); \r\n if (type(p) <> DOM_POLY || op(p, 3) = Expr) && stdlib::hasfloat(p) then\r\n p := numeric::rationalize(p); \r\n Float := proc(l)\r\n local i;\r\n begin\r\n for i from 2 to nops(l) step 2 do\r\n if type(l[i]) = DOM_POLY then\r\n l[i] := mapcoeffs(l[i], float)\r\n else \r\n l[i] := float(l[i])\r\n end_if\r\n end_for; \r\n l\r\n end_proc\r\n else \r\n Float := id\r\n end_if; \r\n unextend := id; \r\n if options[\"UseAlgebraicExtension\"] then\r\n p := poly(p); \r\n T := op(p, 3); \r\n if T = Expr then\r\n if map({coeff(p)}, domtype) minus {DOM_RAT, DOM_INT} = {} then\r\n T := Dom::Rational\r\n else \r\n T := Dom::Fraction(Dom::Polynomial(Dom::Rational))\r\n end_if\r\n end_if; \r\n inds := indets(poly2list(p)); \r\n [pr, ratsubsts, minpol] := [rationalize(poly2list(p), FindRelations = [\"_power\", \"exp\"], MinimalPolynomials)]; \r\n if ratsubsts = {} || traperror((T := fp::fold((p, d) -> Dom::AlgebraicExtension(d, poly(p, [op(indets(p) minus inds)], d)), T)(op(minpol)))) <> 0 || traperror((p := poly(pr, op(p, 2), T))) <> 0 || p = FAIL then\r\n p := pp\r\n else \r\n unextend := (if pp::dom = DOM_POLY then\r\n proc(f)\r\n local i;\r\n begin\r\n evalAt([(if op(pp, 3) = Expr then\r\n expr(f[1])\r\n else \r\n coerce(f[1], op(pp, 3))\r\n end_if), (poly(f[i], op(pp, 3)), f[i + 1]) $ i = 2..nops(f) - 1 step 2], ratsubsts)\r\n end_proc\r\n else \r\n proc(f)\r\n local i;\r\n begin\r\n evalAt([expr(f[1]), (expr(f[i]), f[i + 1]) $ i = 2..nops(f) - 1 step 2], ratsubsts)\r\n end_proc\r\n end_if)\r\n end_if\r\n end_if; \r\n if p::dom::sqrfree <> FAIL then\r\n return(p::dom::sqrfree(p))\r\n end_if; \r\n if domtype(p) = DOM_POLY then\r\n if testargs() then\r\n t := op(p, 3); \r\n if domtype(t) = DOM_DOMAIN then\r\n if t::hasProp <> FAIL then\r\n if t::hasProp(Cat::FactorialDomain) then\r\n if t::characteristic <> 0 then\r\n if t::hasProp(Cat::Field) then\r\n if ~t::hasProp(Dom::IntegerMod) then\r\n if ~t::hasProp(Dom::GaloisField) then\r\n if ~t::hasProp(Dom::AlgebraicExtension) || t::degreeOverPrimeField = UNKNOWN then\r\n error(message(\"symbolic:polylib:NotAFiniteField\"))\r\n end_if\r\n end_if\r\n end_if\r\n else \r\n error(message(\"symbolic:polylib:NotAField\"))\r\n end_if\r\n end_if\r\n else \r\n error(message(\"symbolic:polylib:NotAFactorialDomain\"))\r\n end_if\r\n end_if\r\n else \r\n if t <> hold(Expr) && ~isprime(op(t, 1)) then\r\n error(message(\"symbolic:polylib:NoPrimeModulus\"))\r\n end_if\r\n end_if\r\n end_if; \r\n ret := Float(recollect(unextend(faclib::sqrfree_poly(p, options)))); \r\n Factored::create(ret, \"squarefree\")\r\n else \r\n ret := Float(recollect(unextend(faclib::factor_expr(p, options, TRUE)))); \r\n Factored::create(ret, \"squarefree\")\r\n end_if\r\n end_proc@normal)\r\ngives \r\n 2*a + 4*x*y + (3*y^2 + a)^2/(x - y)^2 + x^2 + 10*y^2 + (6*y*(3*y^2 + a))/(x - y) \r\nApplying the rule\r\n Simplify::sqrfreeFactor\r\ngives \r\n (x^2 + x*y + y^2 + a)^2/(x - y)^2 \r\nEND OF PROOF \r\n
I don't understand what the proof for simplify is doing I was just trying to get the steps how do I just get the like mathematica/wolfram alpha show steps output
