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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 B, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, i
from proveit.core_expr_types import A_1_to_m, B_1_to_i, C_1_to_n
from proveit.linear_algebra import VecAdd
from proveit.logic import Equals, Implies, InClass
from proveit.numbers import one
from proveit.physics.quantum import Qmult, QmultCodomain
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Qmult(A_1_to_m, VecAdd(B_1_to_i), C_1_to_n)
expr = ExprTuple(Lambda([A_1_to_m, B_1_to_i, C_1_to_n], Implies(InClass(sub_expr2, QmultCodomain), Equals(sub_expr2, VecAdd(ExprRange(sub_expr1, Qmult(A_1_to_m, IndexedVar(B, sub_expr1), C_1_to_n), one, i))).with_wrapping_at(2)).with_wrapping_at(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(A_{1}, A_{2}, \ldots, A_{m}, B_{1}, B_{2}, \ldots, B_{i}, C_{1}, C_{2}, \ldots, C_{n}\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \left(\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace \left(B_{1} +  B_{2} +  \ldots +  B_{i}\right)\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right) \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace \left(B_{1} +  B_{2} +  \ldots +  B_{i}\right)\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) =  \\ \left(\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace B_{1}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) +  \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace B_{2}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) +  \ldots +  \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace B_{i}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right)\right) \end{array} \end{array}\right) \end{array} \end{array}\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
1Lambdaparameters: 2
body: 3
2ExprTuple29, 22, 31
3Operationoperator: 4
operands: 5
4Literal
5ExprTuple6, 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operands: 11
8Literal
9ExprTuple13, 12
10Literal
11ExprTuple13, 14
12Literal
13Operationoperator: 26
operands: 15
14Operationoperator: 19
operands: 16
15ExprTuple29, 17, 31
16ExprTuple18
17Operationoperator: 19
operands: 20
18ExprRangelambda_map: 21
start_index: 37
end_index: 25
19Literal
20ExprTuple22
21Lambdaparameter: 40
body: 23
22ExprRangelambda_map: 24
start_index: 37
end_index: 25
23Operationoperator: 26
operands: 27
24Lambdaparameter: 45
body: 28
25Variable
26Literal
27ExprTuple29, 30, 31
28IndexedVarvariable: 34
index: 45
29ExprRangelambda_map: 32
start_index: 37
end_index: 33
30IndexedVarvariable: 34
index: 40
31ExprRangelambda_map: 36
start_index: 37
end_index: 38
32Lambdaparameter: 45
body: 39
33Variable
34Variable
35ExprTuple40
36Lambdaparameter: 45
body: 41
37Literal
38Variable
39IndexedVarvariable: 42
index: 45
40Variable
41IndexedVarvariable: 43
index: 45
42Variable
43Variable
44ExprTuple45
45Variable