logo

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, Lambda, X
from proveit.linear_algebra import Hspace, LinMap
from proveit.logic import Forall, InSet
from proveit.physics.quantum import Qmult, var_ket_psi
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(A, Conditional(Forall(instance_param_or_params = [var_ket_psi], instance_expr = InSet(Qmult(A, var_ket_psi), X), domain = Hspace), InSet(Qmult(A), LinMap(Hspace, X)))))
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(A \mapsto \left\{\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(A \thinspace \lvert \psi \rangle\right) \in X\right) \textrm{ if } \left[A\right] \in \mathcal{L}\left(\mathcal{H}, X\right)\right..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 26
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 8
4Operationoperator: 19
operands: 7
5Literal
6ExprTuple8
7ExprTuple9, 10
8Lambdaparameter: 27
body: 12
9Operationoperator: 24
operand: 26
10Operationoperator: 14
operands: 15
11ExprTuple27
12Conditionalvalue: 16
condition: 17
13ExprTuple26
14Literal
15ExprTuple23, 22
16Operationoperator: 19
operands: 18
17Operationoperator: 19
operands: 20
18ExprTuple21, 22
19Literal
20ExprTuple27, 23
21Operationoperator: 24
operands: 25
22Variable
23Variable
24Literal
25ExprTuple26, 27
26Variable
27Variable