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 ExprTuple, k, m
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.numbers import Exp, Mult, e, frac, i, one, 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 = frac(one, Exp(two, frac(_t, two)))
sub_expr4 = VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, _t)), domain = _m_domain)
expr = ExprTuple(Qmult(sub_expr1, sub_expr3, sub_expr2, sub_expr4), Qmult(Qmult(sub_expr1, sub_expr3, sub_expr2), sub_expr4))

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({_{t}}\langle m \rvert \thinspace \frac{1}{2^{\frac{t}{2}}} \thinspace {\mathrm {FT}}^{\dag}_{t} \thinspace \left(\sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right)\right), \left({_{t}}\langle m \rvert \thinspace \frac{1}{2^{\frac{t}{2}}} \thinspace {\mathrm {FT}}^{\dag}_{t}\right) \thinspace \left(\sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right)\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 7 operands: 3
2	Operation	operator: 7 operands: 4
3	ExprTuple	11, 12, 13, 6
4	ExprTuple	5, 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operand: 14
7	Literal
8	ExprTuple	11, 12, 13
9	Literal
10	ExprTuple	14
11	Operation	operator: 15 operands: 16
12	Operation	operator: 35 operands: 17
13	Operation	operator: 18 operand: 61
14	Lambda	parameter: 53 body: 21
15	Literal
16	ExprTuple	22, 61
17	ExprTuple	62, 23
18	Literal
19	ExprTuple	61
20	ExprTuple	53
21	Conditional	value: 24 condition: 25
22	Variable
23	Operation	operator: 56 operands: 26
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operands: 30
26	ExprTuple	60, 31
27	Literal
28	ExprTuple	32, 33
29	Literal
30	ExprTuple	53, 34
31	Operation	operator: 35 operands: 36
32	Operation	operator: 56 operands: 37
33	Operation	operator: 38 operands: 39
34	Operation	operator: 40 operands: 41
35	Literal
36	ExprTuple	61, 60
37	ExprTuple	42, 43
38	Literal
39	ExprTuple	53, 61
40	Literal
41	ExprTuple	44, 45
42	Literal
43	Operation	operator: 46 operands: 47
44	Literal
45	Operation	operator: 48 operands: 49
46	Literal
47	ExprTuple	60, 50, 51, 52, 53
48	Literal
49	ExprTuple	54, 55
50	Literal
51	Literal
52	Literal
53	Variable
54	Operation	operator: 56 operands: 57
55	Operation	operator: 58 operand: 62
56	Literal
57	ExprTuple	60, 61
58	Literal
59	ExprTuple	62
60	Literal
61	Literal
62	Literal