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, ScalarMult(sub_expr3, Qmult(sub_expr2, sub_expr4))), Qmult(sub_expr3, sub_expr1, 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 \left(\frac{1}{2^{\frac{t}{2}}} \cdot \left({\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)\right)\right), \frac{1}{2^{\frac{t}{2}}} \thinspace {_{t}}\langle m \rvert \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)\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: 14 operands: 3
2	Operation	operator: 14 operands: 4
3	ExprTuple	6, 5
4	ExprTuple	10, 6, 17, 18
5	Operation	operator: 32 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 63
10	Operation	operator: 26 operands: 13
11	Operation	operator: 14 operands: 15
12	Variable
13	ExprTuple	64, 16
14	Literal
15	ExprTuple	17, 18
16	Operation	operator: 58 operands: 19
17	Operation	operator: 20 operand: 63
18	Operation	operator: 22 operand: 25
19	ExprTuple	62, 24
20	Literal
21	ExprTuple	63
22	Literal
23	ExprTuple	25
24	Operation	operator: 26 operands: 27
25	Lambda	parameter: 55 body: 29
26	Literal
27	ExprTuple	63, 62
28	ExprTuple	55
29	Conditional	value: 30 condition: 31
30	Operation	operator: 32 operands: 33
31	Operation	operator: 34 operands: 35
32	Literal
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	55, 38
36	Operation	operator: 58 operands: 39
37	Operation	operator: 40 operands: 41
38	Operation	operator: 42 operands: 43
39	ExprTuple	44, 45
40	Literal
41	ExprTuple	55, 63
42	Literal
43	ExprTuple	46, 47
44	Literal
45	Operation	operator: 48 operands: 49
46	Literal
47	Operation	operator: 50 operands: 51
48	Literal
49	ExprTuple	62, 52, 53, 54, 55
50	Literal
51	ExprTuple	56, 57
52	Literal
53	Literal
54	Literal
55	Variable
56	Operation	operator: 58 operands: 59
57	Operation	operator: 60 operand: 64
58	Literal
59	ExprTuple	62, 63
60	Literal
61	ExprTuple	64
62	Literal
63	Literal
64	Literal