- new
-
Create a new zero polynomial and return it to the caller.
- copy OBJREF
-
Perform a deep copy of the polynomial object referenced by OBJREF.
- monOrder
-
- monOrder STRING
-
Return the current monomial ordering. If an argument is passed, it is assigned as the new monomial ordering. The valid orderings are:
tdeg - total degree (single variable case only)
lex - pure lexicographic ordering
grlex - graded lex
grevlex - graded reverse lex
- varOrder
-
- varOrder ARRAYREF
-
Return the current variable ordering as an array reference. If an argument is passed, it is assigned as the new variable ordering. For example,
$poly->varOrder(['x','y','z']);
assigns the variable ordering x > y > z.
- monomials
-
- monomials HASHREF
-
Returns the current collection of monomials. If an argument is passed, it is assigned as the new collection of monomials.
- insertMonomial OBJREF
-
Performs a copy of the monomial referred to by OBJREF and inserts it into the monomial collection.
- simplify
-
Attempt to unify monomials with the same 'signature' (see getSignature) through addition.
- fromString STRING
-
Construct the state of the polynomial from the algebraic expressin represented in STRING. For example,
$poly->fromString("xyz+x^2y^4+x+2");
would create four monomials: xyz, x^2y^4, x, and 2. The previous monomials contained in the polynomial are destroyed.
- toString
-
Convert the current state of the polynomial into a string and return it to the caller. This string can be sent back in via fromString and be used to reconstruct the polynomial.
- applyOrder
-
Order the monomials according to the current monomial ordering setting.
- SortByLexOrder
-
(Internal) Perform sort.
- SortByGrevLex
-
(Internal) Perform sort.
- SortByGrLex
-
(Internal) Perform sort.
- SortByTotalDegree
-
(Internal) Perform sort.
- getLT
-
Get the leading term of the polynomial and return it to the caller.
- isNotZero
-
Return a boolean indiciating wether or not the polynomial is a zero polynomial or not.
- mult OBJREF
-
Perform polynomial multiplication using this polynomial and the one referred to by OBJREF. Return a new polynomial containing the product.
- add OBJREF
-
Perform polynomial addition using this polynomial and the one referred to by OBJREF. Return a new polynomial containing the sum.
- subtract OBJREF
-
Perform polynomial subtraction using this polynomial and the one referred to by OBJREF. Return a new polynomial containing the difference.
- divide OBJREF
-
Perform polynomial division using this polynomial and the one referred to by OBJREF. Return an array reference containing the quotients and the remainder.
- gcd OBJREF
-
Determine the polynomial greatest common divisor with respect to this polynomial and the one referred to by OBJREF. Return a new polynomial containing the gcd.
- reduce
-
Attempt to achieve two goals:
1) Get as many 1's as coefficients as possible
2) If the leading term's coefficient is negative multiply all the coefficients by -1.
- spoly
-
Determine the polynomial SPOLY with respect to this polynomial and the one referred to by OBJREF. Return a new polynomial containing the SPOLY.