Difference between revisions of "ApCoCoA-1:NCo.BSubtract"
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<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | ||
<par/> | <par/> | ||
| − | Please set ring environment <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>word ordering</em> via the functions <ref>ApCoCoA-1:NCo.SetX|NCo.SetX</ref> and <ref>ApCoCoA-1:NCo.SetOrdering|NCo.SetOrdering</ref>, respectively, before calling this function. The default ordering is the length-lexicographic ordering ( | + | Please set ring environment <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>word ordering</em> via the functions <ref>ApCoCoA-1:NCo.SetX|NCo.SetX</ref> and <ref>ApCoCoA-1:NCo.SetOrdering|NCo.SetOrdering</ref>, respectively, before calling this function. The default ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions. |
<itemize> | <itemize> | ||
| − | <item>@param <em>F1, F2:</em> two polynomials in the free monoid ring <tt>F_{2}<X></tt>, which are left and right operands of subtraction, respectively. Each polynomial is represented as a LIST of words (or terms). Each word is represented as a STRING. For example, <tt>xy^2x</tt> is represented as | + | <item>@param <em>F1, F2:</em> two polynomials in the free monoid ring <tt>F_{2}<X></tt>, which are left and right operands of subtraction, respectively. Each polynomial is represented as a LIST of words (or terms). Each word is represented as a STRING. For example, <tt>xy^2x</tt> is represented as "xyyx", and the identity is represented as the empty string "". Thus, the polynomial <tt>f=xy-y+1</tt> is represented as F:=["xy", "y", ""]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> |
<item>@return: a LIST which represents the polynomial equal to <tt>F1-F2</tt>. Note that we have <tt>F1-F2=F2+F2</tt> over <tt>F_{2}</tt>.</item> | <item>@return: a LIST which represents the polynomial equal to <tt>F1-F2</tt>. Note that we have <tt>F1-F2=F2+F2</tt> over <tt>F_{2}</tt>.</item> | ||
</itemize> | </itemize> | ||
<example> | <example> | ||
| − | NCo.SetX( | + | NCo.SetX("xX"); |
| − | NCo.SetOrdering( | + | NCo.SetOrdering("LLEX"); |
| − | F1:=[ | + | F1:=["xX",""]; |
| − | F2:=[ | + | F2:=["Xx",""]; |
NCo.BSubtract(F1,F2); | NCo.BSubtract(F1,F2); | ||
| − | [ | + | ["xX", "Xx"] |
------------------------------- | ------------------------------- | ||
NCo.BSubtract(F1,F1); | NCo.BSubtract(F1,F1); | ||
| Line 28: | Line 28: | ||
------------------------------- | ------------------------------- | ||
NCo.BSubtract([],F1); | NCo.BSubtract([],F1); | ||
| − | [ | + | ["xX", ""] |
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
Latest revision as of 13:38, 29 October 2020
| This article is about a function from ApCoCoA-1. |
NCo.BSubtract
Subtraction of two polynomials in a free monoid ring over the binary field F_{2}={0,1}.
Syntax
NCo.BSubtract(F1:LIST, F2:LIST):LIST
Description
Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.
Please set ring environment alphabet (or set of indeterminates) X and word ordering via the functions NCo.SetX and NCo.SetOrdering, respectively, before calling this function. The default ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param F1, F2: two polynomials in the free monoid ring F_{2}<X>, which are left and right operands of subtraction, respectively. Each polynomial is represented as a LIST of words (or terms). Each word is represented as a STRING. For example, xy^2x is represented as "xyyx", and the identity is represented as the empty string "". Thus, the polynomial f=xy-y+1 is represented as F:=["xy", "y", ""]. The zero polynomial 0 is represented as the empty LIST [].
@return: a LIST which represents the polynomial equal to F1-F2. Note that we have F1-F2=F2+F2 over F_{2}.
Example
NCo.SetX("xX");
NCo.SetOrdering("LLEX");
F1:=["xX",""];
F2:=["Xx",""];
NCo.BSubtract(F1,F2);
["xX", "Xx"]
-------------------------------
NCo.BSubtract(F1,F1);
[ ]
-------------------------------
NCo.BSubtract([],F1);
["xX", ""]
-------------------------------
See also
