Inheritance diagram for PyClical.clifford:

Collaboration diagram for PyClical.clifford:

Public Member Functions
def	__cinit__ (self, other=0, ixt=None)

def	__dealloc__ (self)

def	__contains__ (self, x)

def	__iter__ (self)

def	reframe (self, ixt)

def	__richcmp__ (lhs, rhs, int, op)

def	__getitem__ (self, ixt)

def	__neg__ (self)

def	__pos__ (self)

def	__add__ (lhs, rhs)

def	__iadd__ (self, rhs)

def	__sub__ (lhs, rhs)

def	__isub__ (self, rhs)

def	__mul__ (lhs, rhs)

def	__imul__ (self, rhs)

def	__mod__ (lhs, rhs)

def	__imod__ (self, rhs)

def	__and__ (lhs, rhs)

def	__iand__ (self, rhs)

def	__xor__ (lhs, rhs)

def	__ixor__ (self, rhs)

def	__div__ (lhs, rhs)

def	__idiv__ (self, rhs)

def	inv (self)

def	__or__ (lhs, rhs)

def	__ior__ (self, rhs)

def	__pow__ (self, m, dummy)

def	pow (self, m)

def	outer_pow (self, m)

def	__call__ (self, grade)

def	scalar (self)

def	pure (self)

def	even (self)

def	odd (self)

def	vector_part (self, frm=None)

def	involute (self)

def	reverse (self)

def	conj (self)

def	quad (self)

def	norm (self)

def	abs (self)

def	max_abs (self)

def	truncated (self, limit)

def	isnan (self)

def	frame (self)

def	__repr__ (self)

def	__str__ (self)

Public Attributes
	instance

Detailed Description

Python class clifford wraps C++ class Clifford.

Definition at line 532 of file PyClical.pyx.

Member Function Documentation

◆ add()

def PyClical.clifford.__add__	(	lhs,
		rhs
	)

Geometric sum.

>>> print clifford(1) + clifford("{2}")
1+{2}
>>> print clifford("{1}") + clifford("{2}")
{1}+{2}

Definition at line 739 of file PyClical.pyx.

◆ and()

def PyClical.clifford.__and__	(	lhs,
		rhs
	)

Inner product.

>>> print clifford("{1}") & clifford("{2}")
0
>>> print clifford(2) & clifford("{2}")
0
>>> print clifford("{1}") & clifford("{1}")
1
>>> print clifford("{1}") & clifford("{1,2}")
{2}

Definition at line 835 of file PyClical.pyx.

◆ call()

def PyClical.clifford.__call__	(	self,
		grade
	)

Pure grade-vector part.

>>> print clifford("{1}")(1)
{1}
>>> print clifford("{1}")(0)
0
>>> print clifford("1+{1}+{1,2}")(0)
1
>>> print clifford("1+{1}+{1,2}")(1)
{1}
>>> print clifford("1+{1}+{1,2}")(2)
{1,2}
>>> print clifford("1+{1}+{1,2}")(3)
0

Definition at line 1019 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ cinit()

def PyClical.clifford.__cinit__	(	self,
		other = `0`,
		ixt = `None`
	)

Construct an object of type clifford.

>>> print clifford(2)
2
>>> print clifford(2L)
2
>>> print clifford(2.0)
2
>>> print clifford(1.0e-1)
0.1
>>> print clifford("2")
2
>>> print clifford("2{1,2,3}")
2{1,2,3}
>>> print clifford(clifford("2{1,2,3}"))
2{1,2,3}
>>> print clifford("-{1}")
-{1}
>>> print clifford(2,index_set({1,2}))
2{1,2}
>>> print clifford([2,3],index_set({1,2}))
2{1}+3{2}

Definition at line 563 of file PyClical.pyx.

◆ contains()

def PyClical.clifford.__contains__	(	self,
		x
	)

Not applicable.

>>> x=clifford(index_set({-3,4,7})); -3 in x
Traceback (most recent call last):
  ...
TypeError: Not applicable.

Definition at line 626 of file PyClical.pyx.

◆ dealloc()

def PyClical.clifford.__dealloc__ ( self )

Clean up by deallocating the instance of C++ class Clifford.

Definition at line 620 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ div()

def PyClical.clifford.__div__	(	lhs,
		rhs
	)

Geometric quotient.

>>> print clifford("{1}") / clifford("{2}")
{1,2}
>>> print clifford(2) / clifford("{2}")
2{2}
>>> print clifford("{1}") / clifford("{1}")
1
>>> print clifford("{1}") / clifford("{1,2}")
-{2}

Definition at line 895 of file PyClical.pyx.

◆ getitem()

def PyClical.clifford.__getitem__	(	self,
		ixt
	)

Subscripting: map from index set to scalar coordinate.

>>> clifford("{1}")[index_set(1)]
1.0
>>> clifford("{1}")[index_set({1})]
1.0
>>> clifford("{1}")[index_set({1,2})]
0.0
>>> clifford("2{1,2}")[index_set({1,2})]
2.0

Definition at line 706 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ iadd()

def PyClical.clifford.__iadd__	(	self,
		rhs
	)

Geometric sum.

>>> x = clifford(1); x += clifford("{2}"); print x
1+{2}

Definition at line 750 of file PyClical.pyx.

◆ iand()

def PyClical.clifford.__iand__	(	self,
		rhs
	)

Inner product.

>>> x = clifford("{1}"); x &= clifford("{2}"); print x
0
>>> x = clifford(2); x &= clifford("{2}"); print x
0
>>> x = clifford("{1}"); x &= clifford("{1}"); print x
1
>>> x = clifford("{1}"); x &= clifford("{1,2}"); print x
{2}

Definition at line 850 of file PyClical.pyx.

◆ idiv()

def PyClical.clifford.__idiv__	(	self,
		rhs
	)

Geometric quotient.

>>> x = clifford("{1}"); x /= clifford("{2}"); print x
{1,2}
>>> x = clifford(2); x /= clifford("{2}"); print x
2{2}
>>> x = clifford("{1}"); x /= clifford("{1}"); print x
1
>>> x = clifford("{1}"); x /= clifford("{1,2}"); print x
-{2}

Definition at line 910 of file PyClical.pyx.

◆ imod()

def PyClical.clifford.__imod__	(	self,
		rhs
	)

Contraction.

>>> x = clifford("{1}"); x %= clifford("{2}"); print x
0
>>> x = clifford(2); x %= clifford("{2}"); print x
2{2}
>>> x = clifford("{1}"); x %= clifford("{1}"); print x
1
>>> x = clifford("{1}"); x %= clifford("{1,2}"); print x
{2}

Definition at line 820 of file PyClical.pyx.

◆ imul()

def PyClical.clifford.__imul__	(	self,
		rhs
	)

Geometric product.

>>> x = clifford(2); x *= clifford("{2}"); print x
2{2}
>>> x = clifford("{1}"); x *= clifford("{2}"); print x
{1,2}
>>> x = clifford("{1}"); x *= clifford("{1,2}"); print x
{2}

Definition at line 792 of file PyClical.pyx.

◆ ior()

def PyClical.clifford.__ior__	(	self,
		rhs
	)

Transform left hand side, using right hand side as a transformation.

>>> x=clifford("{1,2}") * pi/2; y=clifford("{1}"); y|=x; print y
-{1}
>>> x=clifford("{1,2}") * pi/2; y=clifford("{1}"); y|=exp(x); print y
-{1}

Definition at line 949 of file PyClical.pyx.

◆ isub()

def PyClical.clifford.__isub__	(	self,
		rhs
	)

Geometric difference.

>>> x = clifford(1); x -= clifford("{2}"); print x
1-{2}

Definition at line 770 of file PyClical.pyx.

◆ iter()

def PyClical.clifford.__iter__ ( self )

Not applicable.

>>> for a in clifford(index_set({-3,4,7})): print a,
Traceback (most recent call last):
  ...
TypeError: Not applicable.

Definition at line 637 of file PyClical.pyx.

◆ ixor()

def PyClical.clifford.__ixor__	(	self,
		rhs
	)

Outer product.

>>> x = clifford("{1}"); x ^= clifford("{2}"); print x
{1,2}
>>> x = clifford(2); x ^= clifford("{2}"); print x
2{2}
>>> x = clifford("{1}"); x ^= clifford("{1}"); print x
0
>>> x = clifford("{1}"); x ^= clifford("{1,2}"); print x
0

Definition at line 880 of file PyClical.pyx.

◆ mod()

def PyClical.clifford.__mod__	(	lhs,
		rhs
	)

Contraction.

>>> print clifford("{1}") % clifford("{2}")
0
>>> print clifford(2) % clifford("{2}")
2{2}
>>> print clifford("{1}") % clifford("{1}")
1
>>> print clifford("{1}") % clifford("{1,2}")
{2}

Definition at line 805 of file PyClical.pyx.

◆ mul()

def PyClical.clifford.__mul__	(	lhs,
		rhs
	)

Geometric product.

>>> print clifford("{1}") * clifford("{2}")
{1,2}
>>> print clifford(2) * clifford("{2}")
2{2}
>>> print clifford("{1}") * clifford("{1,2}")
{2}

Definition at line 779 of file PyClical.pyx.

◆ neg()

def PyClical.clifford.__neg__ ( self )

Unary -.

>>> print -clifford("{1}")
-{1}

Definition at line 721 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ or()

def PyClical.clifford.__or__	(	lhs,
		rhs
	)

Transform left hand side, using right hand side as a transformation.

>>> x=clifford("{1,2}") * pi/2; y=clifford("{1}"); print y|x
-{1}
>>> x=clifford("{1,2}") * pi/2; y=clifford("{1}"); print y|exp(x)
-{1}

Definition at line 938 of file PyClical.pyx.

◆ pos()

def PyClical.clifford.__pos__ ( self )

Unary +.

>>> print +clifford("{1}")
{1}

Definition at line 730 of file PyClical.pyx.

◆ pow()

def PyClical.clifford.__pow__	(	self,
		m,
		dummy
	)

Power: self to the m.

>>> x=clifford("{1}"); print x ** 2
1
>>> x=clifford("2"); print x ** 2
4
>>> x=clifford("2+{1}"); print x ** 0
1
>>> x=clifford("2+{1}"); print x ** 1
2+{1}
>>> x=clifford("2+{1}"); print x ** 2
5+4{1}
>>> i=clifford("{1,2}");print exp(pi/2) * (i ** i)
1

Definition at line 960 of file PyClical.pyx.

References PyClical.clifford.pow().

◆ repr()

def PyClical.clifford.__repr__ ( self )

The “official” string representation of self.

>>> clifford("1+3{-1}+2{1,2}+4{-2,7}").__repr__()
'clifford("1+3{-1}+2{1,2}+4{-2,7}")'

Definition at line 1225 of file PyClical.pyx.

References clifford_to_repr().

◆ richcmp()

def PyClical.clifford.__richcmp__	(	lhs,
		rhs,
		int,
		op
	)

Compare objects of type clifford.

>>> clifford("{1}") == clifford("1{1}")
True
>>> clifford("{1}") != clifford("1.0{1}")
False
>>> clifford("{1}") != clifford("1.0")
True
>>> clifford("{1,2}") == None
False
>>> clifford("{1,2}") != None
True
>>> None == clifford("{1,2}")
False
>>> None != clifford("{1,2}")
True

Definition at line 671 of file PyClical.pyx.

◆ str()

def PyClical.clifford.__str__ ( self )

The “informal” string representation of self.

>>> clifford("1+3{-1}+2{1,2}+4{-2,7}").__str__()
'1+3{-1}+2{1,2}+4{-2,7}'

Definition at line 1234 of file PyClical.pyx.

References clifford_to_str().

◆ sub()

def PyClical.clifford.__sub__	(	lhs,
		rhs
	)

Geometric difference.

>>> print clifford(1) - clifford("{2}")
1-{2}
>>> print clifford("{1}") - clifford("{2}")
{1}-{2}

Definition at line 759 of file PyClical.pyx.

◆ xor()

def PyClical.clifford.__xor__	(	lhs,
		rhs
	)

Outer product.

>>> print clifford("{1}") ^ clifford("{2}")
{1,2}
>>> print clifford(2) ^ clifford("{2}")
2{2}
>>> print clifford("{1}") ^ clifford("{1}")
0
>>> print clifford("{1}") ^ clifford("{1,2}")
0

Definition at line 865 of file PyClical.pyx.

◆ abs()

def PyClical.clifford.abs ( self )

Absolute value: square root of norm.

>>> clifford("1+{-1}+{1,2}+{1,2,3}").abs()
2.0

Definition at line 1174 of file PyClical.pyx.

References glucat.abs().

◆ conj()

def PyClical.clifford.conj ( self )

Conjugation, reverse o involute == involute o reverse.

>>> print (clifford("{1}")).conj()
-{1}
>>> print (clifford("{2}") * clifford("{1}")).conj()
{1,2}
>>> print (clifford("{1}") * clifford("{2}")).conj()
-{1,2}
>>> print clifford("1+{1}+{1,2}").conj()
1-{1}-{1,2}

Definition at line 1137 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ even()

def PyClical.clifford.even ( self )

Even part of multivector, sum of even grade terms.

>>> print clifford("1+{1}+{1,2}").even()
1+{1,2}

Definition at line 1060 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ frame()

def PyClical.clifford.frame ( self )

Subalgebra generated by all generators of terms of given multivector.

>>> print clifford("1+3{-1}+2{1,2}+4{-2,7}").frame()
{-2,-1,1,2,7}
>>> s=clifford("1+3{-1}+2{1,2}+4{-2,7}").frame(); type(s)
<type 'PyClical.index_set'>

Definition at line 1214 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ inv()

def PyClical.clifford.inv ( self )

Geometric multiplicative inverse.

>>> x = clifford("{1}"); print x.inv()
{1}
>>> x = clifford(2); print x.inv()
0.5
>>> x = clifford("{1,2}"); print x.inv()
-{1,2}

Definition at line 925 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ involute()

def PyClical.clifford.involute ( self )

Main involution, each {i} is replaced by -{i} in each term,
eg. clifford("{1}") -> -clifford("{1}").

>>> print clifford("{1}").involute()
-{1}
>>> print (clifford("{2}") * clifford("{1}")).involute()
-{1,2}
>>> print (clifford("{1}") * clifford("{2}")).involute()
{1,2}
>>> print clifford("1+{1}+{1,2}").involute()
1-{1}+{1,2}

Definition at line 1106 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ isnan()

def PyClical.clifford.isnan ( self )

Check if a multivector contains any IEEE NaN values.

>>> clifford().isnan()
False

Definition at line 1205 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ max_abs()

def PyClical.clifford.max_abs ( self )

Maximum of absolute values of components of multivector: multivector infinity norm.

>>> clifford("1+{-1}+{1,2}+{1,2,3}").max_abs()
1.0
>>> clifford("3+2{1}+{1,2}").max_abs()
3.0

Definition at line 1183 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ norm()

def PyClical.clifford.norm ( self )

Norm == sum of squares of coordinates.

>>> clifford("1+{1}+{1,2}").norm()
3.0
>>> clifford("1+{-1}+{1,2}+{1,2,3}").norm()
4.0

Definition at line 1163 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ odd()

def PyClical.clifford.odd ( self )

Odd part of multivector, sum of odd grade terms.

>>> print clifford("1+{1}+{1,2}").odd()
{1}

Definition at line 1069 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ outer_pow()

def PyClical.clifford.outer_pow	(	self,
		m
	)

Outer product power.

>>> x=clifford("2+{1}"); print x.outer_pow(0)
1
>>> x=clifford("2+{1}"); print x.outer_pow(1)
2+{1}
>>> x=clifford("2+{1}"); print x.outer_pow(2)
4+4{1}
>>> print clifford("1+{1}+{1,2}").outer_pow(3)
1+3{1}+3{1,2}

Definition at line 1003 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ pow()

def PyClical.clifford.pow	(	self,
		m
	)

Power: self to the m.

>>> x=clifford("{1}"); print x.pow(2)
1
>>> x=clifford("2"); print x.pow(2)
4
>>> x=clifford("2+{1}"); print x.pow(0)
1
>>> x=clifford("2+{1}"); print x.pow(1)
2+{1}
>>> x=clifford("2+{1}"); print x.pow(2)
5+4{1}
>>> print clifford("1+{1}+{1,2}").pow(3)
1+3{1}+3{1,2}
>>> i=clifford("{1,2}");print exp(pi/2) * i.pow(i)
1

Definition at line 979 of file PyClical.pyx.

References glucat.exp(), PyClical.index_set.instance, PyClical.clifford.instance, and glucat.log().

Referenced by PyClical.clifford.__pow__().

◆ pure()

def PyClical.clifford.pure ( self )

Pure part.

>>> print clifford("1+{1}+{1,2}").pure()
{1}+{1,2}
>>> print clifford("{1,2}").pure()
{1,2}

Definition at line 1049 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ quad()

def PyClical.clifford.quad ( self )

Quadratic form == (rev(x)*x)(0).

>>> print clifford("1+{1}+{1,2}").quad()
3.0
>>> print clifford("1+{-1}+{1,2}+{1,2,3}").quad()
2.0

Definition at line 1152 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ reframe()

def PyClical.clifford.reframe	(	self,
		ixt
	)

Put self into a larger frame, containing the union of self.frame() and index set ixt.
This can be used to make multiplication faster, by multiplying within a common frame.

>>> clifford("2+3{1}").reframe(index_set({1,2,3}))
clifford("2+3{1}")
>>> s=index_set({1,2,3});t=index_set({-3,-2,-1});x=random_clifford(s); x.reframe(t).frame() == (s|t);
True

Definition at line 648 of file PyClical.pyx.

◆ reverse()

def PyClical.clifford.reverse ( self )

Reversion, eg. clifford("{1}")*clifford("{2}") -> clifford("{2}")*clifford("{1}").

>>> print clifford("{1}").reverse()
{1}
>>> print (clifford("{2}") * clifford("{1}")).reverse()
{1,2}
>>> print (clifford("{1}") * clifford("{2}")).reverse()
-{1,2}
>>> print clifford("1+{1}+{1,2}").reverse()
1+{1}-{1,2}

Definition at line 1122 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ scalar()

def PyClical.clifford.scalar ( self )

Scalar part.

>>> clifford("1+{1}+{1,2}").scalar()
1.0
>>> clifford("{1,2}").scalar()
0.0

Definition at line 1038 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ truncated()

def PyClical.clifford.truncated	(	self,
		limit
	)

Remove all terms of self with relative size smaller than limit.

>>> clifford("1e8+{1}+1e-8{1,2}").truncated(1.0e-6)
clifford("100000000")
>>> clifford("1e4+{1}+1e-4{1,2}").truncated(1.0e-6)
clifford("10000+{1}")

Definition at line 1194 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

◆ vector_part()

def PyClical.clifford.vector_part	(	self,
		frm = `None`
	)

Vector part of multivector, as a Python list, with respect to frm.

>>> print clifford("1+2{1}+3{2}+4{1,2}").vector_part()
[2.0, 3.0]
>>> print clifford("1+2{1}+3{2}+4{1,2}").vector_part(index_set({-1,1,2}))
[0.0, 2.0, 3.0]

Definition at line 1078 of file PyClical.pyx.

References PyClical.index_set.instance, and PyClical.clifford.instance.

Member Data Documentation

◆ instance

The documentation for this class was generated from the following file:

pyclical/PyClical.pyx

Public Member Functions

Public Attributes

Detailed Description

Member Function Documentation

◆ __add__()

◆ __and__()

◆ __call__()

◆ __cinit__()

◆ __contains__()

◆ __dealloc__()

◆ __div__()

◆ __getitem__()

◆ __iadd__()

◆ __iand__()

◆ __idiv__()

◆ __imod__()

◆ __imul__()

◆ __ior__()

◆ __isub__()

◆ __iter__()

◆ __ixor__()

◆ __mod__()

◆ __mul__()

◆ __neg__()

◆ __or__()

◆ __pos__()

◆ __pow__()

◆ __repr__()

◆ __richcmp__()

◆ __str__()

◆ __sub__()

◆ __xor__()

◆ abs()

◆ conj()

◆ even()

◆ frame()

◆ inv()

◆ involute()

◆ isnan()

◆ max_abs()

◆ norm()

◆ odd()

◆ outer_pow()

◆ pow()

◆ pure()

◆ quad()

◆ reframe()

◆ reverse()

◆ scalar()

◆ truncated()

◆ vector_part()

Member Data Documentation

◆ instance

◆ add()

◆ and()

◆ call()

◆ cinit()

◆ contains()

◆ dealloc()

◆ div()

◆ getitem()

◆ iadd()

◆ iand()

◆ idiv()

◆ imod()

◆ imul()

◆ ior()

◆ isub()

◆ iter()

◆ ixor()

◆ mod()

◆ mul()

◆ neg()

◆ or()

◆ pos()

◆ pow()

◆ repr()

◆ richcmp()

◆ str()

◆ sub()

◆ xor()