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Expression of type Lambda

from the theory of proveit.physics.quantum.algebra

In [1]:
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, Conditional, Function, Lambda, X
from proveit.linear_algebra import LinMap
from proveit.logic import And, Equals, Forall, InClass, InSet
from proveit.physics.quantum import HilbertSpaces, Qmult, var_ket_psi
from proveit.physics.quantum.algebra import Hspace
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [var_ket_psi]
sub_expr2 = Qmult(A)
expr = Lambda([Hspace, X], Conditional(Forall(instance_param_or_params = [A], instance_expr = Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Qmult(A, var_ket_psi), Function(sub_expr2, sub_expr1)), domain = Hspace), condition = InSet(sub_expr2, LinMap(Hspace, X))), And(InClass(Hspace, HilbertSpaces), InClass(X, HilbertSpaces))))
Out[2]:
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\mathcal{H}, X\right) \mapsto \left\{\forall_{A~|~\left[A\right] \in \mathcal{L}\left(\mathcal{H}, X\right)}~\left[\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(A \thinspace \lvert \psi \rangle\right) = \left[A\right]\left(\lvert \psi \rangle\right)\right)\right] \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}\right..
In [5]:
stored_expr.style_options()
Out[5]:
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
Out[6]:
 core typesub-expressionsexpression
0Lambdaparameters: 24
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 17
operand: 7
3Operationoperator: 5
operands: 6
4ExprTuple7
5Literal
6ExprTuple8, 9
7Lambdaparameter: 41
body: 10
8Operationoperator: 12
operands: 11
9Operationoperator: 12
operands: 13
10Conditionalvalue: 14
condition: 15
11ExprTuple34, 16
12Literal
13ExprTuple27, 16
14Operationoperator: 17
operand: 20
15Operationoperator: 30
operands: 19
16Literal
17Literal
18ExprTuple20
19ExprTuple36, 21
20Lambdaparameter: 40
body: 22
21Operationoperator: 23
operands: 24
22Conditionalvalue: 25
condition: 26
23Literal
24ExprTuple34, 27
25Operationoperator: 28
operands: 29
26Operationoperator: 30
operands: 31
27Variable
28Literal
29ExprTuple32, 33
30Literal
31ExprTuple40, 34
32Operationoperator: 38
operands: 35
33Operationoperator: 36
operand: 40
34Variable
35ExprTuple41, 40
36Operationoperator: 38
operand: 41
37ExprTuple40
38Literal
39ExprTuple41
40Variable
41Variable