|
glucat 0.12.0
|


Public Member Functions | |
| __cinit__ (self, other=0, ixt=None) | |
| __dealloc__ (self) | |
| __contains__ (self, x) | |
| __iter__ (self) | |
| reframe (self, ixt) | |
| __richcmp__ (lhs, rhs, int, op) | |
| __getitem__ (self, ixt) | |
| __neg__ (self) | |
| __pos__ (self) | |
| __add__ (lhs, rhs) | |
| __iadd__ (self, rhs) | |
| __sub__ (lhs, rhs) | |
| __isub__ (self, rhs) | |
| __mul__ (lhs, rhs) | |
| __imul__ (self, rhs) | |
| __mod__ (lhs, rhs) | |
| __imod__ (self, rhs) | |
| __and__ (lhs, rhs) | |
| __iand__ (self, rhs) | |
| __xor__ (lhs, rhs) | |
| __ixor__ (self, rhs) | |
| __truediv__ (lhs, rhs) | |
| __idiv__ (self, rhs) | |
| inv (self) | |
| __or__ (lhs, rhs) | |
| __ior__ (self, rhs) | |
| __pow__ (self, m, dummy) | |
| pow (self, m) | |
| outer_pow (self, m) | |
| __call__ (self, grade) | |
| scalar (self) | |
| pure (self) | |
| even (self) | |
| odd (self) | |
| vector_part (self, frm=None) | |
| involute (self) | |
| reverse (self) | |
| conj (self) | |
| quad (self) | |
| norm (self) | |
| abs (self) | |
| max_abs (self) | |
| truncated (self, limit) | |
| isinf (self) | |
| isnan (self) | |
| frame (self) | |
| __repr__ (self) | |
| __str__ (self) | |
Public Attributes | |
| instance = new Clifford((<clifford>other).unwrap()) | |
Python class clifford wraps C++ class Clifford.
Definition at line 537 of file PyClical.pyx.
| PyClical.clifford.__add__ | ( | lhs, | |
| rhs ) |
Geometric sum.
>>> print(clifford(1) + clifford("{2}"))
1+{2}
>>> print(clifford("{1}") + clifford("{2}"))
{1}+{2}
Definition at line 740 of file PyClical.pyx.
| 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 836 of file PyClical.pyx.
| 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 1020 of file PyClical.pyx.
References PyClical.clifford.instance, and PyClical.index_set.instance.
| PyClical.clifford.__cinit__ | ( | self, | |
| other = 0, | |||
| ixt = None ) |
Construct an object of type clifford.
>>> print(clifford(2))
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 565 of file PyClical.pyx.
| 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 627 of file PyClical.pyx.
| PyClical.clifford.__dealloc__ | ( | self | ) |
Clean up by deallocating the instance of C++ class Clifford.
Definition at line 621 of file PyClical.pyx.
References PyClical.clifford.instance, and PyClical.index_set.instance.
| 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 707 of file PyClical.pyx.
References PyClical.clifford.instance, and PyClical.index_set.instance.
| PyClical.clifford.__iadd__ | ( | self, | |
| rhs ) |
Geometric sum.
>>> x = clifford(1); x += clifford("{2}"); print(x)
1+{2}
Definition at line 751 of file PyClical.pyx.
| 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 851 of file PyClical.pyx.
| 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 911 of file PyClical.pyx.
| 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 821 of file PyClical.pyx.
| 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 793 of file PyClical.pyx.
| 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 950 of file PyClical.pyx.
| PyClical.clifford.__isub__ | ( | self, | |
| rhs ) |
Geometric difference.
>>> x = clifford(1); x -= clifford("{2}"); print(x)
1-{2}
Definition at line 771 of file PyClical.pyx.
| PyClical.clifford.__iter__ | ( | self | ) |
Not applicable.
>>> for a in clifford(index_set({-3,4,7})):print(a, end=",")
Traceback (most recent call last):
...
TypeError: Not applicable.
Definition at line 638 of file PyClical.pyx.
| 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 881 of file PyClical.pyx.
| 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 806 of file PyClical.pyx.
| 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 780 of file PyClical.pyx.
| PyClical.clifford.__neg__ | ( | self | ) |
Unary -.
>>> print(-clifford("{1}"))
-{1}
Definition at line 722 of file PyClical.pyx.
References PyClical.clifford.instance, and PyClical.index_set.instance.
| 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 939 of file PyClical.pyx.
| PyClical.clifford.__pos__ | ( | self | ) |
Unary +.
>>> print(+clifford("{1}"))
{1}
Definition at line 731 of file PyClical.pyx.
| 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 961 of file PyClical.pyx.
References PyClical.clifford.pow().
| 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 1235 of file PyClical.pyx.
References clifford_to_repr().
| 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 672 of file PyClical.pyx.
| 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 1244 of file PyClical.pyx.
References clifford_to_str().
| PyClical.clifford.__sub__ | ( | lhs, | |
| rhs ) |
Geometric difference.
>>> print(clifford(1) - clifford("{2}"))
1-{2}
>>> print(clifford("{1}") - clifford("{2}"))
{1}-{2}
Definition at line 760 of file PyClical.pyx.
| PyClical.clifford.__truediv__ | ( | 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 896 of file PyClical.pyx.
| 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 866 of file PyClical.pyx.
| PyClical.clifford.abs | ( | self | ) |
Absolute value: square root of norm.
>>> clifford("1+{-1}+{1,2}+{1,2,3}").abs()
2.0
Definition at line 1175 of file PyClical.pyx.
References glucat.abs().
| 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 1138 of file PyClical.pyx.
References PyClical.clifford.conj(), PyClical.clifford.instance, and PyClical.index_set.instance.
Referenced by PyClical.clifford.conj().
| 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 1061 of file PyClical.pyx.
References PyClical.clifford.even(), PyClical.clifford.instance, and PyClical.index_set.instance.
Referenced by PyClical.clifford.even().
| 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)
<class 'PyClical.index_set'>
Definition at line 1224 of file PyClical.pyx.
References PyClical.clifford.frame(), PyClical.clifford.instance, and PyClical.index_set.instance.
Referenced by PyClical.clifford.frame().
| 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 926 of file PyClical.pyx.
References PyClical.clifford.instance, PyClical.index_set.instance, and PyClical.clifford.inv().
Referenced by PyClical.clifford.inv().
| 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 1107 of file PyClical.pyx.
References PyClical.clifford.instance, PyClical.index_set.instance, and PyClical.clifford.involute().
Referenced by PyClical.clifford.involute().
| PyClical.clifford.isinf | ( | self | ) |
Check if a multivector contains any infinite values. >>> clifford().isinf() False
Definition at line 1206 of file PyClical.pyx.
References PyClical.clifford.instance, PyClical.index_set.instance, and PyClical.clifford.isnan().
| PyClical.clifford.isnan | ( | self | ) |
Check if a multivector contains any IEEE NaN values. >>> clifford().isnan() False
Definition at line 1215 of file PyClical.pyx.
References PyClical.clifford.instance, PyClical.index_set.instance, and PyClical.clifford.isnan().
Referenced by PyClical.clifford.isinf(), and PyClical.clifford.isnan().
| 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 1184 of file PyClical.pyx.
References PyClical.clifford.instance, PyClical.index_set.instance, and PyClical.clifford.max_abs().
Referenced by PyClical.clifford.max_abs().
| 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 1164 of file PyClical.pyx.
References PyClical.clifford.instance, PyClical.index_set.instance, and PyClical.clifford.norm().
Referenced by PyClical.clifford.norm().
| PyClical.clifford.odd | ( | self | ) |
Odd part of multivector, sum of odd grade terms.
>>> print(clifford("1+{1}+{1,2}").odd())
{1}
Definition at line 1070 of file PyClical.pyx.
References PyClical.clifford.instance, PyClical.index_set.instance, and PyClical.clifford.odd().
Referenced by PyClical.clifford.odd().
| 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 1004 of file PyClical.pyx.
References PyClical.clifford.instance, PyClical.index_set.instance, and PyClical.clifford.outer_pow().
Referenced by PyClical.clifford.outer_pow().
| 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 980 of file PyClical.pyx.
References PyClical.clifford.instance, PyClical.index_set.instance, and PyClical.clifford.pow().
Referenced by PyClical.clifford.__pow__(), and PyClical.clifford.pow().
| 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 1050 of file PyClical.pyx.
References PyClical.clifford.instance, PyClical.index_set.instance, and PyClical.clifford.pure().
Referenced by PyClical.clifford.pure().
| 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 1153 of file PyClical.pyx.
References PyClical.clifford.instance, PyClical.index_set.instance, and PyClical.clifford.quad().
Referenced by PyClical.clifford.quad().
| 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 649 of file PyClical.pyx.
| 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 1123 of file PyClical.pyx.
References PyClical.clifford.instance, PyClical.index_set.instance, and PyClical.clifford.reverse().
Referenced by PyClical.clifford.reverse().
| PyClical.clifford.scalar | ( | self | ) |
Scalar part.
>>> clifford("1+{1}+{1,2}").scalar()
1.0
>>> clifford("{1,2}").scalar()
0.0
Definition at line 1039 of file PyClical.pyx.
References PyClical.clifford.instance, PyClical.index_set.instance, and PyClical.clifford.scalar().
Referenced by PyClical.clifford.scalar().
| 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 1195 of file PyClical.pyx.
References PyClical.clifford.instance, PyClical.index_set.instance, and PyClical.clifford.truncated().
Referenced by PyClical.clifford.truncated().
| 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 1079 of file PyClical.pyx.
References PyClical.clifford.instance, PyClical.index_set.instance, and PyClical.clifford.vector_part().
Referenced by PyClical.clifford.vector_part().
Definition at line 592 of file PyClical.pyx.
Referenced by PyClical.clifford.__call__(), PyClical.index_set.__contains__(), PyClical.clifford.__dealloc__(), PyClical.index_set.__dealloc__(), PyClical.clifford.__getitem__(), PyClical.index_set.__getitem__(), PyClical.index_set.__invert__(), PyClical.clifford.__neg__(), PyClical.index_set.__setitem__(), PyClical.clifford.conj(), PyClical.index_set.count(), PyClical.index_set.count_neg(), PyClical.index_set.count_pos(), PyClical.clifford.even(), PyClical.clifford.frame(), PyClical.index_set.hash_fn(), PyClical.clifford.inv(), PyClical.clifford.involute(), PyClical.clifford.isinf(), PyClical.clifford.isnan(), PyClical.index_set.max(), PyClical.clifford.max_abs(), PyClical.index_set.min(), PyClical.clifford.norm(), PyClical.clifford.odd(), PyClical.clifford.outer_pow(), PyClical.clifford.pow(), PyClical.clifford.pure(), PyClical.clifford.quad(), PyClical.clifford.reverse(), PyClical.clifford.scalar(), PyClical.index_set.sign_of_mult(), PyClical.index_set.sign_of_square(), PyClical.clifford.truncated(), and PyClical.clifford.vector_part().