Îõ³h*¢ Q'      !"#$%&0.2.0.0#Multivariate polynomials on a ring.(c) Stéphane Laurent, 2023GPL-3laurent_step@outlook.fr Safe-Inferred 3ÂÃÄÅÆÝ ç6'hsprayappend trailing zeros(hspray,append trailing zeros to get the same lengthhsprayAddition of two sprayshspraySubstraction of two sprayshsprayMultiply two sprays hsprayPower of a spray hsprayScale spray by a scalar hsprayScale spray by an integer)hspraydrop trailing zeros*hspray,drop trailing zeros in the powers of a spray+hspray%simplify powers and remove zero terms,hsprayaddition of two sprays-hsprayopposite spray.hsprayscale a spray by a scalar/hsprayderivative of a monomial hsprayDerivative of a spray0hspraymultiply two monomials1hspraymultiply two sprays hspray-Spray corresponding to the basic monomial x_nhspray Unit sprayhsprayConstant spray2hsprayevaluates a monomialhsprayEvaluate a spray3hsprayspray from monomial4hspraynumber of variables in a spray5hspray'substitute some variables in a monomialhspray$Substitute some variables in a sprayhsprayÎConvert a spray with rational coefficients to a spray with double coefficients6hspray helper for hspray*Compose a spray with a change of variableshspray!Create a spray from list of terms7hspray(prettyPowers "x" [0, 2, 1] = x^(0, 2, 1)hsprayPretty form of a spray8hspray"prettyPowers' [0, 2, 1] = "x2^2x3"hspray9Pretty form of a spray, with monomials showed as "x1x3^2"9hspray!prettyPowersXYZ [1, 2, 1] = XY^2Zhspray5Pretty form of a spray having at more three variableshsprayTerms of a sprayhspray Spray as listhspray*Bombieri spray (for internal usage in the  scubature library):hsprayindex of the maximum of a listhsprayLeading term of a spray ;hspray+whether a monomial divides another monomial<hspray:quotient of monomial Q by monomial p, assuming P divides QhsprayïRemainder of the division of a spray by a list of divisors, using the lexicographic ordering of the monomials=hsprayslight modification of  to speed up groebner00>hspray+groebner basis, not minimal and not reduced?hspray'groebner basis, minimal but not reduced@hsprayreduce a Groebner basishspray4Groebner basis (always minimal and possibly reduced)Ahspray.generate all permutations of a binary sequencehsprayElementary symmetric polynomialhspray)Whether a spray is a symmetric polynomial hspray–Whether a spray can be written as a polynomial of a given list of sprays; the sprays in the list must belong to the same polynomial ring as the spray hspray(index of the variable of differentiationhspray the sprayhspray6function mapping a coefficient to a string, typically Bhspray(a string denoting the variable, e.g. "x"hspray the sprayhspraylist of sprays hspray#whether to return the reduced basishspraynumber of variableshsprayindex!     !     667 8 7 7Ã      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFÇ%hspray-0.2.0.0-7VK47kOlc5wEPYqLKeSOAzMath.Algebra.HsprayhsprayMonomialSprayPowers exponents nvariables^+^^-^^*^^**^*^.^ derivSpraylone unitSpray constantSpray evalSpraysubstituteSprayfromRationalSpray composeSprayfromList prettySpray prettySpray'prettySprayXYZ sprayTermstoList bombieriSpray leadingTerm sprayDivisiongroebner esPolynomialisSymmetricSprayisPolynomialOf$fHashablePowers $fEqPowers $fCHashMap $fCaHashMap $fCHashMap0 $fShowPowers growSequence harmonizesimplifyPowers simplifySpray cleanSpray addSprays negateSpray scaleSpray derivMonomial multMonomial multSprays evalMonomial fromMonomialnumberOfVariablessubstituteMonomialidentify prettyPowers prettyPowers'prettyPowersXYZmaxIndexdividesquotientsprayDivision' groebner00 groebner0reduceGroebnerBasispermutationsBinarySequencebaseGHC.Showshow