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, k, m
from proveit.linear_algebra import ScalarMult
from proveit.logic import 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 = Qmult(NumBra(m, _t), InverseFourierTransform(_t), ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, _t)))
expr = ExprTuple(Conditional(sub_expr1, InSet(k, _m_domain)), sub_expr1)

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 {\mathrm {FT}}^{\dag}_{t} \thinspace \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right) \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}, {_{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)

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	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9, 10
6	Literal
7	ExprTuple	43, 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operand: 45
10	Operation	operator: 16 operands: 17
11	Operation	operator: 18 operands: 19
12	Literal
13	ExprTuple	20, 45
14	Literal
15	ExprTuple	45
16	Literal
17	ExprTuple	21, 22
18	Literal
19	ExprTuple	23, 24
20	Variable
21	Operation	operator: 36 operands: 25
22	Operation	operator: 26 operands: 27
23	Literal
24	Operation	operator: 28 operands: 29
25	ExprTuple	30, 31
26	Literal
27	ExprTuple	43, 45
28	Literal
29	ExprTuple	32, 33
30	Literal
31	Operation	operator: 34 operands: 35
32	Operation	operator: 36 operands: 37
33	Operation	operator: 38 operand: 46
34	Literal
35	ExprTuple	44, 40, 41, 42, 43
36	Literal
37	ExprTuple	44, 45
38	Literal
39	ExprTuple	46
40	Literal
41	Literal
42	Literal
43	Variable
44	Literal
45	Literal
46	Literal