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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 Conditional, ExprTuple, Lambda
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, InSet
from proveit.physics.quantum import Qmult, bra_varphi, ket_varphi, var_ket_psi, var_ket_v, varphi
from proveit.physics.quantum.algebra import Hspace
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(varphi, Conditional(Equals(Qmult(var_ket_psi, bra_varphi), Lambda(var_ket_v, Conditional(ScalarMult(Qmult(bra_varphi, var_ket_v), var_ket_psi), InSet(var_ket_v, Hspace)))), InSet(ket_varphi, Hspace))))
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(\varphi \mapsto \left\{\left(\lvert \psi \rangle \thinspace \langle \varphi \rvert\right) = \left[\lvert v \rangle \mapsto \left\{\left(\langle \varphi \rvert \thinspace \lvert v \rangle\right) \cdot \lvert \psi \rangle \textrm{ if } \lvert v \rangle \in \mathcal{H}\right..\right] \textrm{ if } \lvert \varphi \rangle \in \mathcal{H}\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
1Lambdaparameter: 30
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 19
operands: 7
5Literal
6ExprTuple8, 9
7ExprTuple10, 23
8Operationoperator: 24
operands: 11
9Lambdaparameter: 27
body: 13
10Operationoperator: 14
operand: 30
11ExprTuple22, 26
12ExprTuple27
13Conditionalvalue: 15
condition: 16
14Literal
15Operationoperator: 17
operands: 18
16Operationoperator: 19
operands: 20
17Literal
18ExprTuple21, 22
19Literal
20ExprTuple27, 23
21Operationoperator: 24
operands: 25
22Variable
23Variable
24Literal
25ExprTuple26, 27
26Operationoperator: 28
operand: 30
27Variable
28Literal
29ExprTuple30
30Variable