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Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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(\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..\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
0ExprTuple1
1Lambdaparameters: 25
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 18
operand: 8
4Operationoperator: 6
operands: 7
5ExprTuple8
6Literal
7ExprTuple9, 10
8Lambdaparameter: 42
body: 11
9Operationoperator: 13
operands: 12
10Operationoperator: 13
operands: 14
11Conditionalvalue: 15
condition: 16
12ExprTuple35, 17
13Literal
14ExprTuple28, 17
15Operationoperator: 18
operand: 21
16Operationoperator: 31
operands: 20
17Literal
18Literal
19ExprTuple21
20ExprTuple37, 22
21Lambdaparameter: 41
body: 23
22Operationoperator: 24
operands: 25
23Conditionalvalue: 26
condition: 27
24Literal
25ExprTuple35, 28
26Operationoperator: 29
operands: 30
27Operationoperator: 31
operands: 32
28Variable
29Literal
30ExprTuple33, 34
31Literal
32ExprTuple41, 35
33Operationoperator: 39
operands: 36
34Operationoperator: 37
operand: 41
35Variable
36ExprTuple42, 41
37Operationoperator: 39
operand: 42
38ExprTuple41
39Literal
40ExprTuple42
41Variable
42Variable