6051
(|AlgebraicFunction| R F)
|package|
(((|AlgebraicFunction| |#1| |#2|)
(CATEGORY |package|
(SIGNATURE |rootOf| (|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)))
(SIGNATURE |operator| ((|BasicOperator|) (|BasicOperator|)))
(SIGNATURE |belong?| ((|Boolean|) (|BasicOperator|)))
(SIGNATURE |inrootof| (|#2| (|SparseUnivariatePolynomial| |#2|) |#2|))
(SIGNATURE |droot| ((|OutputForm|) (|List| |#2|)))
(IF (|has| |#1| (|RetractableTo| (|Integer|)))
(PROGN
(SIGNATURE ** (|#2| |#2| (|Fraction| (|Integer|))))
(SIGNATURE |minPoly|
((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)))
(SIGNATURE |definingPolynomial| (|#2| |#2|))
(SIGNATURE |iroot| (|#2| |#1| (|Integer|))))
|%noBranch|))
(|IntegralDomain|) (|FunctionSpace| |#1|))
(T |AlgebraicFunction|))
(NIL T T)
"algfunc.spad"
((|iroot| (*1 *2 *3 *4)
(AND (|isDomain| *4 (|Integer|)) (|ofCategory| *2 (|FunctionSpace| *3))
(|isDomain| *1 (|AlgebraicFunction| *3 *2))
(|ofCategory| *3 (|RetractableTo| *4))
(|ofCategory| *3 (|IntegralDomain|))))
(|definingPolynomial| (*1 *2 *2)
(AND (|ofCategory| *3 (|RetractableTo| (|Integer|)))
(|ofCategory| *3 (|IntegralDomain|))
(|isDomain| *1 (|AlgebraicFunction| *3 *2))
(|ofCategory| *2 (|FunctionSpace| *3))))
(|minPoly| (*1 *2 *3)
(AND (|isDomain| *3 (|Kernel| *5)) (|ofCategory| *5 (|FunctionSpace| *4))
(|ofCategory| *4 (|RetractableTo| (|Integer|)))
(|ofCategory| *4 (|IntegralDomain|))
(|isDomain| *2 (|SparseUnivariatePolynomial| *5))
(|isDomain| *1 (|AlgebraicFunction| *4 *5))))
(** (*1 *2 *2 *3)
(AND (|isDomain| *3 (|Fraction| (|Integer|)))
(|ofCategory| *4 (|RetractableTo| (|Integer|)))
(|ofCategory| *4 (|IntegralDomain|))
(|isDomain| *1 (|AlgebraicFunction| *4 *2))
(|ofCategory| *2 (|FunctionSpace| *4))))
(|droot| (*1 *2 *3)
(AND (|isDomain| *3 (|List| *5)) (|ofCategory| *5 (|FunctionSpace| *4))
(|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|OutputForm|))
(|isDomain| *1 (|AlgebraicFunction| *4 *5))))
(|inrootof| (*1 *2 *3 *2)
(AND (|isDomain| *3 (|SparseUnivariatePolynomial| *2))
(|ofCategory| *2 (|FunctionSpace| *4))
(|ofCategory| *4 (|IntegralDomain|))
(|isDomain| *1 (|AlgebraicFunction| *4 *2))))
(|belong?| (*1 *2 *3)
(AND (|isDomain| *3 (|BasicOperator|)) (|ofCategory| *4 (|IntegralDomain|))
(|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|AlgebraicFunction| *4 *5))
(|ofCategory| *5 (|FunctionSpace| *4))))
(|operator| (*1 *2 *2)
(AND (|isDomain| *2 (|BasicOperator|)) (|ofCategory| *3 (|IntegralDomain|))
(|isDomain| *1 (|AlgebraicFunction| *3 *4))
(|ofCategory| *4 (|FunctionSpace| *3))))
(|rootOf| (*1 *2 *3 *4)
(AND (|isDomain| *3 (|SparseUnivariatePolynomial| *2))
(|isDomain| *4 (|Symbol|)) (|ofCategory| *2 (|FunctionSpace| *5))
(|isDomain| *1 (|AlgebraicFunction| *5 *2))
(|ofCategory| *5 (|IntegralDomain|)))))
((|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) 39 T ELT))
(|operator| (((|BasicOperator|) (|BasicOperator|)) 53 T ELT))
(|minPoly|
(((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) 148
(|has| |#1| (|RetractableTo| (|Integer|))) ELT))
(|iroot|
((|#2| |#1| (|Integer|)) 120 (|has| |#1| (|RetractableTo| (|Integer|))) ELT))
(|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) 29 T ELT))
(|droot| (((|OutputForm|) (|List| |#2|)) 87 T ELT))
(|definingPolynomial|
((|#2| |#2|) 143 (|has| |#1| (|RetractableTo| (|Integer|))) ELT))
(|belong?| (((|Boolean|) (|BasicOperator|)) 17 T ELT))
(**
((|#2| |#2| (|Fraction| (|Integer|))) 96
(|has| |#1| (|RetractableTo| (|Integer|))) ELT)))
((|AF;minPoly;KSup;25| #1=((|SparseUnivariatePolynomial| F) (|Kernel| F)))
(|AF;droot;LOf;24| #2=((|OutputForm|) (|List| F))) (|AF;minPoly;KSup;23| #1#)
(|AF;definingPolynomial;2F;22| (F F)) (|AF;iroot;RIF;20| #3=(F R (|Integer|)))
(|AF;iroot;RIF;19| #3#) (|AF;iroot;RIF;18| #3#) (|AF;iroot;RIF;17| #3#)
(|AF;**;FFF;13| (F F (|Fraction| (|Integer|)))) (|AF;droot;LOf;11| #2#)
(|AF;inrootof;Sup2F;9| #4=(F (|SparseUnivariatePolynomial| F) F))
(|AF;inrootof;Sup2F;7| #4#)
(|AF;operator;2Bo;6| ((|BasicOperator|) (|BasicOperator|)))
(|AF;rootOf;SupSF;3| (F (|SparseUnivariatePolynomial| F) (|Symbol|)))
(|AF;belong?;BoB;1| ((|Boolean|) (|BasicOperator|))))
((|HasCategory| |#1| '(|RetractableTo| (|Integer|))))
AF
((|constructor|
(NIL "This package provides algebraic functions over an integral domain."))
(|iroot|
((|#2| |#1| (|Integer|))
"\\spad{iroot(p, n)} should be a non-exported function."))
(|definingPolynomial|
((|#2| |#2|)
"\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel."))
(|minPoly|
(((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|))
"\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}."))
(**
((|#2| |#2| (|Fraction| (|Integer|)))
"\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}."))
(|droot|
(((|OutputForm|) (|List| |#2|))
"\\spad{droot(l)} should be a non-exported function."))
(|inrootof|
((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|)
"\\spad{inrootof(p, x)} should be a non-exported function."))
(|belong?|
(((|Boolean|) (|BasicOperator|))
"\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator."))
(|operator|
(((|BasicOperator|) (|BasicOperator|))
"\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator."))
(|rootOf|
((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|))
"\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.")))
(("documentation" 0 4507) ("ancestors" 0 NIL) ("parents" 0 NIL)
("abbreviation" 0 4504) ("predicates" 0 4450) ("attributes" 0 NIL)
("signaturesAndLocals" 0 3787) ("superDomain" 0 NIL) ("operationAlist" 0 3058)
("modemaps" 0 880) ("sourceFile" 0 865) ("dualSignature" 0 855)
("constructorModemap" 0 57) ("constructorKind" 0 47) ("constructorForm" 0 21))