Expression of type Lambda ¶

from the theory of proveit.physics.quantum.algebra ¶

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import A, B, Conditional, Lambda, X, Y
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import Exists, InClass, InSet, Set
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
sub_expr1 = LinMap(Hspace, X)
expr = Lambda([A, B], Conditional(Exists(instance_param_or_params = [Hspace, X, Y], instance_expr = InSet([Qmult(A), Qmult(B)], Set([sub_expr1, Hspace], [X, LinMap(Hspace, Complex)], [LinMap(X, Y), sub_expr1], [Complex, QmultCodomain], [QmultCodomain, Complex])), domain = HilbertSpaces), InClass(Qmult(A, B), QmultCodomain)))

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(A, B\right) \mapsto \left\{\exists_{\mathcal{H}, X, Y \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left(\left(\left[A\right], \left[B\right]\right) \in \left\{\left(\mathcal{L}\left(\mathcal{H}, X\right), \mathcal{H}\right), \left(X, \mathcal{L}\left(\mathcal{H}, \mathbb{C}\right)\right), \left(\mathcal{L}\left(X, Y\right), \mathcal{L}\left(\mathcal{H}, X\right)\right), \left(\mathbb{C}, \mathcal{Q^*}\right), \left(\mathcal{Q^*}, \mathbb{C}\right)\right\}\right) \textrm{ if } \left(A \thinspace B\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Lambda	parameters: 11 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 7
3	Operation	operator: 29 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	8, 45
7	Lambda	parameters: 9 body: 10
8	Operation	operator: 32 operands: 11
9	ExprTuple	52, 53, 51
10	Conditional	value: 12 condition: 13
11	ExprTuple	40, 41
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21, 22
18	ExprTuple	23, 24
19	Operation	operator: 25 operands: 26
20	Operation	operator: 29 operands: 27
21	Operation	operator: 29 operands: 28
22	Operation	operator: 29 operands: 30
23	Operation	operator: 32 operand: 40
24	Operation	operator: 32 operand: 41
25	Literal
26	ExprTuple	34, 35, 36, 37, 38
27	ExprTuple	52, 39
28	ExprTuple	53, 39
29	Literal
30	ExprTuple	51, 39
31	ExprTuple	40
32	Literal
33	ExprTuple	41
34	ExprTuple	44, 52
35	ExprTuple	53, 42
36	ExprTuple	43, 44
37	ExprTuple	50, 45
38	ExprTuple	45, 50
39	Literal
40	Variable
41	Variable
42	Operation	operator: 48 operands: 46
43	Operation	operator: 48 operands: 47
44	Operation	operator: 48 operands: 49
45	Literal
46	ExprTuple	52, 50
47	ExprTuple	53, 51
48	Literal
49	ExprTuple	52, 53
50	Literal
51	Variable
52	Variable
53	Variable

Expression of type Lambda¶

from the theory of proveit.physics.quantum.algebra¶

Expression of type Lambda ¶

from the theory of proveit.physics.quantum.algebra ¶