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<TITLE>Polynomial - Perl module implementing an algebraic polynomial</TITLE>
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<LI><A HREF="#NAME">NAME</A>
<LI><A HREF="#DESCRIPTION">DESCRIPTION</A>
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<H1><A NAME="NAME">NAME</A></H1>
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Polynomial - Perl module implementing an algebraic polynomial
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<H1><A NAME="DESCRIPTION">DESCRIPTION</A></H1>
<DL>
<DT><STRONG><A NAME="item_new">new</A></STRONG><DD>
<P>
Create a new zero polynomial and return it to the caller.
<p>
<DT><STRONG><A NAME="item_copy">copy OBJREF</A></STRONG><DD>
<P>
Perform a deep copy of the polynomial object referenced by OBJREF.
<p>
<DT><STRONG><A NAME="item_monOrder">monOrder</A></STRONG><DD>
<DT><STRONG>monOrder STRING</STRONG><DD>
<P>
Return the current monomial ordering. If an argument is passed, it is
assigned as the new monomial ordering. The valid orderings are:
<P>
<PRE> tdeg - total degree (single variable case only)
lex - pure lexicographic ordering
grlex - graded lex
grevlex - graded reverse lex
</PRE>
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<DT><STRONG><A NAME="item_varOrder">varOrder</A></STRONG><DD>
<DT><STRONG>varOrder ARRAYREF</STRONG><DD>
<P>
Return the current variable ordering as an array reference. If an argument
is passed, it is assigned as the new variable ordering. For example,
<P>
<PRE> $poly->varOrder(['x','y','z']);
</PRE>
<P>
assigns the variable ordering x > y > z.
<p>
<DT><STRONG><A NAME="item_monomials">monomials</A></STRONG><DD>
<DT><STRONG>monomials HASHREF</STRONG><DD>
<P>
Returns the current collection of monomials. If an argument is passed, it
is assigned as the new collection of monomials.
<p>
<DT><STRONG><A NAME="item_insertMonomial">insertMonomial OBJREF</A></STRONG><DD>
<P>
Performs a copy of the monomial referred to by OBJREF and inserts it into
the monomial collection.
<p>
<DT><STRONG><A NAME="item_simplify">simplify</A></STRONG><DD>
<P>
Attempt to unify monomials with the same 'signature' (see getSignature)
through addition.
<p>
<DT><STRONG><A NAME="item_fromString">fromString STRING</A></STRONG><DD>
<P>
Construct the state of the polynomial from the algebraic expressin
represented in STRING. For example,
<P>
<PRE> $poly->fromString("xyz+x^2y^4+x+2");
</PRE>
<P>
would create four monomials: xyz, x^2y^4, x, and 2. The previous monomials
contained in the polynomial are destroyed.
<p>
<DT><STRONG><A NAME="item_toString">toString</A></STRONG><DD>
<P>
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.
<p>
<DT><STRONG><A NAME="item_applyOrder">applyOrder</A></STRONG><DD>
<P>
Order the monomials according to the current monomial ordering setting.
<p>
<DT><STRONG><A NAME="item_SortByLexOrder">SortByLexOrder</A></STRONG><DD>
<P>
(Internal) Perform sort.
<p>
<DT><STRONG><A NAME="item_SortByGrevLex">SortByGrevLex</A></STRONG><DD>
<P>
(Internal) Perform sort.
<p>
<DT><STRONG><A NAME="item_SortByGrLex">SortByGrLex</A></STRONG><DD>
<P>
(Internal) Perform sort.
<p>
<DT><STRONG><A NAME="item_SortByTotalDegree">SortByTotalDegree</A></STRONG><DD>
<P>
(Internal) Perform sort.
<p>
<DT><STRONG><A NAME="item_getLT">getLT</A></STRONG><DD>
<P>
Get the leading term of the polynomial and return it to the caller.
<p>
<DT><STRONG><A NAME="item_isNotZero">isNotZero</A></STRONG><DD>
<P>
Return a boolean indiciating wether or not the polynomial is a zero
polynomial or not.
<p>
<DT><STRONG><A NAME="item_mult">mult OBJREF</A></STRONG><DD>
<P>
Perform polynomial multiplication using this polynomial and the one
referred to by OBJREF. Return a new polynomial containing the product.
<p>
<DT><STRONG><A NAME="item_add">add OBJREF</A></STRONG><DD>
<P>
Perform polynomial addition using this polynomial and the one referred to
by OBJREF. Return a new polynomial containing the sum.
<p>
<DT><STRONG><A NAME="item_subtract">subtract OBJREF</A></STRONG><DD>
<P>
Perform polynomial subtraction using this polynomial and the one referred
to by OBJREF. Return a new polynomial containing the difference.
<p>
<DT><STRONG><A NAME="item_divide">divide OBJREF</A></STRONG><DD>
<P>
Perform polynomial division using this polynomial and the one referred to
by OBJREF. Return an array reference containing the quotients and the
remainder.
<p>
<DT><STRONG><A NAME="item_gcd">gcd OBJREF</A></STRONG><DD>
<P>
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.
<p>
<DT><STRONG><A NAME="item_reduce">reduce</A></STRONG><DD>
<P>
Attempt to achieve two goals:
<P>
<PRE> 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.
</PRE>
<p>
<DT><STRONG><A NAME="item_spoly">spoly</A></STRONG><DD>
<P>
Determine the polynomial SPOLY with respect to this polynomial and the one
referred to by OBJREF. Return a new polynomial containing the SPOLY.
</DL>
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<H1><A NAME="AUTHOR">AUTHOR</A></H1>
<P>
Brian Guarraci <<A
HREF="mailto:bguarrac@hotmail.com">bguarrac@hotmail.com</A>>
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