Difference between revisions of "ApCoCoA-1:BBSGen.Poldeg"
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| + | {{Version|1}} | ||
<command> | <command> | ||
<title>BBSGen.PolDeg</title> | <title>BBSGen.PolDeg</title> | ||
| − | <short_description> | + | <short_description>This function computes the arrow degree of a given homogenous polynomial from the ring K[c](see <ref>ApCoCoA-1:BBSGen.Wmat|BBSGen.Wmat</ref>). |
| Line 8: | Line 9: | ||
<syntax> | <syntax> | ||
| − | BBSGen. Poldeg(F,OO,BO,N,W); | + | BBSGen.Poldeg(F,OO,BO,N,W); |
BBSGen.Poldeg(F:POLY,OO:LIST,BO:LIST,N:INT,W:MAT):VECTOR; | BBSGen.Poldeg(F:POLY,OO:LIST,BO:LIST,N:INT,W:MAT):VECTOR; | ||
</syntax> | </syntax> | ||
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<itemize> | <itemize> | ||
| − | <item>@param A homogeneous polynomial with respect to the arrow grading from the ring K[c], order ideal OO, border BO,number of indeterminates of the polynomial ring K[x_1,...,x_N] and the weight matrix(<ref>BBSGen.Wmat</ref>). | + | <item>@param A homogeneous polynomial with respect to the arrow grading from the ring K[c], order ideal OO, border BO,number of indeterminates of the polynomial ring K[x_1,...,x_N] and the weight matrix(<ref>ApCoCoA-1:BBSGen.Wmat|BBSGen.Wmat</ref>). |
</item> | </item> | ||
| − | <item>@return Degree vector of the given homogenous polynomial wrt. the arrow grading . </item> | + | <item>@return Degree vector of the given homogenous polynomial wrt. the arrow grading. </item> |
</itemize> | </itemize> | ||
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Use R::=QQ[x[1..2]]; | Use R::=QQ[x[1..2]]; | ||
| − | OO:= | + | OO:= $apcocoa/borderbasis.Box([1,1]); |
| − | BO:= | + | BO:=$apcocoa/borderbasis.Border(OO); |
Mu:=Len(OO); | Mu:=Len(OO); | ||
Nu:=Len(BO); | Nu:=Len(BO); | ||
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<types> | <types> | ||
<type>borderbasis</type> | <type>borderbasis</type> | ||
| − | <type> | + | <type>bbsmingensys</type> |
| + | <type>Vector</type> | ||
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
</types> | </types> | ||
| − | <see>BBSGen.Wmat</see> | + | <see>ApCoCoA-1:BBSGen.Wmat|BBSGen.Wmat</see> |
| − | <see>BBSGen.NonTriv</see> | + | <see>ApCoCoA-1:BBSGen.NonTriv|BBSGen.NonTriv</see> |
| − | <see>BBSGen.BBFinder</see> | + | <see>ApCoCoA-1:BBSGen.BBFinder|BBSGen.BBFinder</see> |
| − | <key> | + | <key>Poldeg</key> |
| − | <key>BBSGen. | + | <key>BBSGen.Poldeg</key> |
| − | <key>bbsmingensys. | + | <key>bbsmingensys.Poldeg</key> |
| − | <wiki-category>Package_bbsmingensys</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_bbsmingensys</wiki-category> |
</command> | </command> | ||
Latest revision as of 09:51, 7 October 2020
| This article is about a function from ApCoCoA-1. |
BBSGen.PolDeg
This function computes the arrow degree of a given homogenous polynomial from the ring K[c](see BBSGen.Wmat).
Syntax
BBSGen.Poldeg(F,OO,BO,N,W); BBSGen.Poldeg(F:POLY,OO:LIST,BO:LIST,N:INT,W:MAT):VECTOR;
Description
@param A homogeneous polynomial with respect to the arrow grading from the ring K[c], order ideal OO, border BO,number of indeterminates of the polynomial ring K[x_1,...,x_N] and the weight matrix(BBSGen.Wmat).
@return Degree vector of the given homogenous polynomial wrt. the arrow grading.
Example
Use R::=QQ[x[1..2]]; OO:= $apcocoa/borderbasis.Box([1,1]); BO:=$apcocoa/borderbasis.Border(OO); Mu:=Len(OO); Nu:=Len(BO); N:=Len(Indets()); W:=BBSGen.Wmat(OO,BO,N); Use XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; F:= c[2,4]c[4,1] - c[3,3]c[4,2] - c[2,3] + c[3,4]; BBSGen.Poldeg(F,OO,BO,N,W); R :: Vector(1, 1)
