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 Conditional, ExprTuple, Lambda, k, m
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, InSet
from proveit.numbers import Exp, Mult, e, i, pi, two
from proveit.physics.quantum import NumBra, NumKet, Qmult
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _m_domain, _phase, _t

# build up the expression from sub-expressions
sub_expr1 = NumBra(m, _t)
sub_expr2 = InverseFourierTransform(_t)
sub_expr3 = NumKet(k, _t)
sub_expr4 = Exp(e, Mult(two, pi, i, _phase, k))
expr = ExprTuple(Lambda(k, Conditional(Equals(Qmult(sub_expr1, sub_expr2, ScalarMult(sub_expr4, sub_expr3)), Mult(sub_expr4, Qmult(sub_expr1, sub_expr2, sub_expr3))), InSet(k, _m_domain))))

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(k \mapsto \left\{\left({_{t}}\langle m \rvert \thinspace {\mathrm {FT}}^{\dag}_{t} \thinspace \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right)\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \left({_{t}}\langle m \rvert \thinspace {\mathrm {FT}}^{\dag}_{t} \thinspace \lvert k \rangle_{t}\right)\right) \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\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	Lambda	parameter: 55 body: 3
2	ExprTuple	55
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	55, 12
10	Operation	operator: 23 operands: 13
11	Operation	operator: 49 operands: 14
12	Operation	operator: 15 operands: 16
13	ExprTuple	28, 29, 17
14	ExprTuple	27, 18
15	Literal
16	ExprTuple	19, 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operands: 24
19	Literal
20	Operation	operator: 25 operands: 26
21	Literal
22	ExprTuple	27, 30
23	Literal
24	ExprTuple	28, 29, 30
25	Literal
26	ExprTuple	31, 32
27	Operation	operator: 40 operands: 33
28	Operation	operator: 34 operands: 35
29	Operation	operator: 36 operand: 47
30	Operation	operator: 38 operands: 39
31	Operation	operator: 40 operands: 41
32	Operation	operator: 42 operand: 48
33	ExprTuple	44, 45
34	Literal
35	ExprTuple	46, 47
36	Literal
37	ExprTuple	47
38	Literal
39	ExprTuple	55, 47
40	Literal
41	ExprTuple	51, 47
42	Literal
43	ExprTuple	48
44	Literal
45	Operation	operator: 49 operands: 50
46	Variable
47	Literal
48	Literal
49	Literal
50	ExprTuple	51, 52, 53, 54, 55
51	Literal
52	Literal
53	Literal
54	Literal
55	Variable