Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

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 ExprRange, ExprTuple, Variable, t
from proveit.linear_algebra import MatrixExp, MatrixMult, ScalarMult
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Mult, Neg, e, i, one, pi, two, zero
from proveit.physics.quantum.QPE import _U, _ket_u, _phase

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Exp(two, Neg(sub_expr1))
expr = ExprTuple(ExprRange(sub_expr1, Equals(MatrixMult(MatrixExp(_U, sub_expr2), _ket_u), ScalarMult(Exp(e, Mult(two, pi, i, Mult(sub_expr2, _phase))), _ket_u)), Add(Neg(t), one), zero))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(\left(U^{2^{-\left(-t + 1\right)}} \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(2^{-\left(-t + 1\right)} \cdot \varphi\right)} \cdot \lvert u \rangle\right)\right), \left(\left(U^{2^{-\left(-t + 2\right)}} \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(2^{-\left(-t + 2\right)} \cdot \varphi\right)} \cdot \lvert u \rangle\right)\right), \ldots, \left(\left(U^{2^{-0}} \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(2^{-0} \cdot \varphi\right)} \cdot \lvert u \rangle\right)\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	ExprRange	lambda_map: 2 start_index: 3 end_index: 4
2	Lambda	parameter: 43 body: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13
10	Operation	operator: 41 operand: 19
11	Literal
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	19
15	Literal
16	ExprTuple	20, 22
17	Literal
18	ExprTuple	21, 22
19	Variable
20	Operation	operator: 23 operands: 24
21	Operation	operator: 37 operands: 25
22	Literal
23	Literal
24	ExprTuple	26, 35
25	ExprTuple	27, 28
26	Literal
27	Literal
28	Operation	operator: 33 operands: 29
29	ExprTuple	39, 30, 31, 32
30	Literal
31	Literal
32	Operation	operator: 33 operands: 34
33	Literal
34	ExprTuple	35, 36
35	Operation	operator: 37 operands: 38
36	Literal
37	Literal
38	ExprTuple	39, 40
39	Literal
40	Operation	operator: 41 operand: 43
41	Literal
42	ExprTuple	43
43	Variable