public GMacMultivectorBinding BindBasisVectorCoefToConstant(int index, Expr valueExpr)
{
return(BindCoefToPattern(
GMacMathUtils.BasisVectorId(index),
GMacScalarBinding.CreateConstant(BaseFrameMultivector.Root, valueExpr)
));
}
public GaSymMultivector SetTermCoef(int grade, int index, Expr coef)
{
return(SetTermCoef(
GMacMathUtils.BasisBladeId(grade, index),
coef
));
}
public GaSymMultivector SetTermCoef(int grade, int index, MathematicaScalar coef)
{
return(SetTermCoef(
GMacMathUtils.BasisBladeId(grade, index),
coef.Expression
));
}
public GMacMultivectorBinding BindBasisVectorCoefToVariable(int index)
{
return(BindCoefToPattern(
GMacMathUtils.BasisVectorId(index),
GMacScalarBinding.CreateVariable(BaseFrameMultivector.Root)
));
}
private void GenerateApplyOutermorphismToVectorMacro(AstFrame frameInfo)
{
var inputsText = ComposeMacroInputs(
"om", DefaultStructure.Outermorphism,
"mv", frameInfo.FrameMultivector.Name
);
var commandsList = GMacDslSyntaxFactory.SyntaxElementsList(
GMacDslSyntaxFactory.AssignToLocalVariable("imageMv", "mv.#E1# * om.ImageV1.@G1@")
);
for (var index = 2; index <= frameInfo.VSpaceDimension; index++)
{
var id = GMacMathUtils.BasisVectorId(index - 1);
commandsList.Add(
GMacDslSyntaxFactory.AssignToLocalVariable(
"imageMv",
"imageMv + mv.#E" + id + "# * om.ImageV" + index + ".@G1@"
)
);
}
commandsList.AddEmptyLine();
var commandsText = GMacLanguage.CodeGenerator.GenerateCode(commandsList);
GenerateMacro(
frameInfo,
DefaultMacro.Outermorphism.ApplyToVector,
inputsText,
commandsText,
"imageMv"
);
}
public override string ToString()
{
var tableText = new TableComposer(TargetGaSpaceDimension, TargetGaSpaceDimension);
var basisBladeIds = GMacMathUtils.BasisBladeIDs(TargetVSpaceDimension).ToArray();
foreach (var basisBladeId in basisBladeIds)
{
tableText.ColumnsInfo[basisBladeId].Header = basisBladeId.BasisBladeName();
tableText.RowsInfo[basisBladeId].Header = basisBladeId.BasisBladeName();
}
for (var basisBladeId1 = 0; basisBladeId1 < TargetGaSpaceDimension; basisBladeId1++)
{
for (var basisBladeId2 = 0; basisBladeId2 < TargetGaSpaceDimension; basisBladeId2++)
{
var mv = _basisBladesMaps[basisBladeId1, basisBladeId2];
if (mv != null)
{
tableText.Items[basisBladeId1, basisBladeId2] = mv.ToString();
}
}
}
var text = tableText.ToString();
return(text);
}
public GaSymMultivector AddFactor(int grade, int index, Expr coef)
{
return(AddFactor(
GMacMathUtils.BasisBladeId(grade, index),
coef
));
}
public double this[int grade, int index]
{
get
{
return(this[GMacMathUtils.BasisBladeId(grade, index)]);
}
}
public static GaNumMetricOrthonormal Create(IReadOnlyList <int> basisVectorsSignaturesList)
{
var vSpaceDim = basisVectorsSignaturesList.Count;
var bbsList = new GaNumMetricOrthonormal(vSpaceDim);
bbsList[0] = 1;
for (var m = 0; m < vSpaceDim; m++)
{
var bvs = basisVectorsSignaturesList[m];
if (bvs == 0)
{
continue;
}
bbsList[1 << m] = bvs;
}
var idsSeq = GMacMathUtils.BasisBladeIDsSortedByGrade(vSpaceDim, 2);
foreach (var id in idsSeq)
{
int id1, id2;
id.SplitBySmallestBasisVectorId(out id1, out id2);
bbsList[id] = bbsList[id1] * bbsList[id2];
}
return(bbsList);
}
public static GaSymMultivector CreateSymbolicKVector(int gaSpaceDim, string baseCoefName, int grade)
{
return(CreateSymbolic(
gaSpaceDim,
baseCoefName,
GMacMathUtils.BasisBladeIDsOfGrade(gaSpaceDim.ToVSpaceDimension(), grade)
));
}
public override GaSymMultivectorTerm MapToTerm(int id1, int id2)
{
return(GaSymMultivectorTerm.CreateTerm(
TargetGaSpaceDimension,
id1 ^ id2,
GMacMathUtils.IsNegativeEGp(id1, id2) ? Expr.INT_MINUSONE : Expr.INT_ONE
));
}
public override GaNumMultivectorTerm MapToTerm(int id1, int id2)
{
return(GaNumMultivectorTerm.CreateTerm(
TargetGaSpaceDimension,
id1 ^ id2,
GMacMathUtils.IsNegativeEGp(id1, id2) ? -1.0d : 1.0d
));
}
public GMacMultivectorBinding UnBindCoefs(int grade, IEnumerable <int> indexes)
{
foreach (var index in indexes)
{
_patternDictionary.Remove(GMacMathUtils.BasisBladeId(grade, index));
}
return(this);
}
public Expr this[int grade, int index]
{
get
{
var id = GMacMathUtils.BasisBladeId(grade, index);
return((id == TermId) ? TermCoef : Expr.INT_ZERO);
}
}
public double this[int grade, int index]
{
get
{
var id = GMacMathUtils.BasisBladeId(grade, index);
return((id == TermId) ? TermCoef : 0.0d);
}
}
private void GenerateOutermorphismToLinearTransformMacro(AstFrame frameInfo)
{
var commandsList = GMacDslSyntaxFactory.SyntaxElementsList(
GMacDslSyntaxFactory.DeclareLocalVariable(DefaultStructure.LinearTransform, "newTr"),
GMacDslSyntaxFactory.EmptyLine(),
GMacDslSyntaxFactory.FixedCode("let newTr.ImageE0 = Multivector(#E0# = '1')"),
GMacDslSyntaxFactory.EmptyLine()
);
for (var index = 1; index <= frameInfo.VSpaceDimension; index++)
{
var id = GMacMathUtils.BasisVectorId(index - 1);
commandsList.Add(
GMacDslSyntaxFactory.AssignToLocalVariable(
"newTr.ImageE" + id,
"om.ImageV" + index + ".@G1@"
)
);
}
commandsList.AddEmptyLine();
for (var grade = 2; grade <= frameInfo.VSpaceDimension; grade++)
{
var kvSpaceDim = frameInfo.KvSpaceDimension(grade);
for (var index = 0; index < kvSpaceDim; index++)
{
int id = GMacMathUtils.BasisBladeId(grade, index);
int id1, id2;
id.SplitBySmallestBasisVectorId(out id1, out id2);
commandsList.Add(
GMacDslSyntaxFactory.AssignToLocalVariable(
"newTr.ImageE" + id,
" newTr.ImageE" + id1 + " op newTr.ImageE" + id2
)
);
}
commandsList.AddEmptyLine();
}
var commandsText = GMacLanguage.CodeGenerator.GenerateCode(commandsList);
GenerateMacro(
frameInfo,
DefaultMacro.Outermorphism.ToLinearTransform,
ComposeMacroInputs("om", DefaultStructure.Outermorphism),
DefaultStructure.LinearTransform,
commandsText,
"newTr"
);
}
public override GaNumMultivectorTerm MapToTerm(int id1, int id2)
{
return(GaNumMultivectorTerm.CreateTerm(
TargetGaSpaceDimension,
id1 ^ id2,
GMacMathUtils.IsNegativeEGp(id1, id2)
? -OrthogonalMetric[id1 & id2]
: OrthogonalMetric[id1 & id2]
));
}
public GaNumMultivector GetNumTerm(int gaSpaceDim, int grade, int index)
{
var mv = GaNumMultivector.CreateZero(gaSpaceDim);
var basisBladeId = GMacMathUtils.BasisBladeId(grade, index);
mv.SetTermCoef(basisBladeId, GetScalar());
return(mv);
}
public override GaSymMultivectorTerm MapToTerm(int id1, int id2)
{
return(GaSymMultivectorTerm.CreateTerm(
TargetGaSpaceDimension,
id1 ^ id2,
GMacMathUtils.IsNegativeEGp(id1, id2)
? Mfs.Minus[OrthonormalMetric.GetExprSignature(id1 & id2)]
: OrthonormalMetric.GetExprSignature(id1 & id2)
));
}
public GaSymMultivector GetSymTerm(int gaSpaceDim, int grade, int index, double minValue, double maxValue)
{
var mv = GaSymMultivector.CreateZero(gaSpaceDim);
var basisBladeId = GMacMathUtils.BasisBladeId(grade, index);
mv.SetTermCoef(basisBladeId, GetSymbolicScalar(minValue, maxValue));
return(mv);
}
public Expr this[int grade, int index]
{
get
{
return(this[GMacMathUtils.BasisBladeId(grade, index)]);
}
set
{
this[GMacMathUtils.BasisBladeId(grade, index)] = value;
}
}
public GaSymMultivector GetSymIntegerKVector(int gaSpaceDim, int grade, int minValue, int maxValue)
{
var mv = GaSymMultivector.CreateZero(gaSpaceDim);
foreach (var basisBladeId in GMacMathUtils.BasisBladeIDsOfGrade(mv.VSpaceDimension, grade))
{
mv.SetTermCoef(basisBladeId, GetIntegerExpr(minValue, maxValue));
}
return(mv);
}
public GaNumMultivector GetNumVector(int gaSpaceDim)
{
var mv = GaNumMultivector.CreateZero(gaSpaceDim);
foreach (var basisBladeId in GMacMathUtils.BasisBladeIDsOfGrade(mv.VSpaceDimension, 1))
{
mv.SetTermCoef(basisBladeId, GetScalar());
}
return(mv);
}
public GaSymMultivector GetSymKVector(int gaSpaceDim, int grade, double maxValue)
{
var mv = GaSymMultivector.CreateZero(gaSpaceDim);
foreach (var basisBladeId in GMacMathUtils.BasisBladeIDsOfGrade(mv.VSpaceDimension, grade))
{
mv.SetTermCoef(basisBladeId, GetSymbolicScalar(maxValue));
}
return(mv);
}
public override GaNumMultivectorTerm MapToTerm(int id1, int id2)
{
return(GaNumMultivectorTerm.CreateTerm(
TargetGaSpaceDimension,
0,
GMacMathUtils.IsNonZeroESp(id1, id2)
? (GMacMathUtils.IsNegativeEGp(id1, id1)
? -OrthogonalMetric[id1]
: OrthogonalMetric[id1])
: 0.0d
));
}
public override GaSymMultivectorTerm MapToTerm(int id1, int id2)
{
return(GaSymMultivectorTerm.CreateTerm(
TargetGaSpaceDimension,
id1 ^ id2,
GMacMathUtils.IsNonZeroEHip(id1, id2)
? (GMacMathUtils.IsNegativeEGp(id1, id2)
? Mfs.Minus[OrthogonalMetric[id1 & id2]]
: OrthogonalMetric[id1 & id2])
: Expr.INT_ZERO
));
}
public virtual IEnumerable <Tuple <int, IGaSymMultivector> > BasisVectorMaps()
{
for (var index = 0; index < DomainVSpaceDimension; index++)
{
var mv = this[GMacMathUtils.BasisBladeId(1, index)];
if (!mv.IsNullOrZero())
{
yield return(new Tuple <int, IGaSymMultivector>(index, mv));
}
}
}
public Expr[] KVectorPartToColumnVector(int grade)
{
var columnVectorLength = GMacMathUtils.KvSpaceDimension(VSpaceDimension, grade);
var columnVector = new Expr[columnVectorLength];
for (var index = 0; index < columnVectorLength; index++)
{
columnVector[index] = this[grade, index];
}
return(columnVector);
}
public double this[int grade, int index]
{
get
{
var id = GMacMathUtils.BasisBladeId(grade, index);
double coef;
_termsDictionary.TryGetValue(id, out coef);
return(coef);
}
}
public override GaSymMultivectorTerm MapToTerm(int id1, int id2)
{
return(GaSymMultivectorTerm.CreateTerm(
TargetGaSpaceDimension,
0,
GMacMathUtils.IsNonZeroESp(id1, id2)
? (GMacMathUtils.IsNegativeEGp(id1, id1)
? Mfs.Minus[OrthonormalMetric.GetExprSignature(id1)]
: OrthonormalMetric.GetExprSignature(id1))
: Expr.INT_ZERO
));
}