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.logic import InSet
from proveit.numbers import Exp, Mod, Mult, Neg, e, frac, i, pi, two
from proveit.physics.quantum.QPE import _m_domain, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = InSet(k, _m_domain)
expr = ExprTuple(Lambda(k, Conditional(Exp(e, Neg(frac(Mult(two, pi, i, k, Mod(m, _two_pow_t)), _two_pow_t))), sub_expr1)), Lambda(k, Conditional(Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t))), 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(k \mapsto \left\{\mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot \left(m ~\textup{mod}~ 2^{t}\right)}{2^{t}}} \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right.., k \mapsto \left\{\mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}} \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\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	Lambda	parameter: 41 body: 3
2	Lambda	parameter: 41 body: 5
3	Conditional	value: 6 condition: 8
4	ExprTuple	41
5	Conditional	value: 7 condition: 8
6	Operation	operator: 47 operands: 9
7	Operation	operator: 47 operands: 10
8	Operation	operator: 11 operands: 12
9	ExprTuple	14, 13
10	ExprTuple	14, 15
11	Literal
12	ExprTuple	41, 16
13	Operation	operator: 36 operand: 21
14	Literal
15	Operation	operator: 36 operand: 22
16	Operation	operator: 19 operands: 20
17	ExprTuple	21
18	ExprTuple	22
19	Literal
20	ExprTuple	23, 24
21	Operation	operator: 26 operands: 25
22	Operation	operator: 26 operands: 27
23	Literal
24	Operation	operator: 28 operands: 29
25	ExprTuple	30, 46
26	Literal
27	ExprTuple	31, 46
28	Literal
29	ExprTuple	46, 32
30	Operation	operator: 34 operands: 33
31	Operation	operator: 34 operands: 35
32	Operation	operator: 36 operand: 42
33	ExprTuple	49, 39, 40, 41, 38
34	Literal
35	ExprTuple	49, 39, 40, 41, 45
36	Literal
37	ExprTuple	42
38	Operation	operator: 43 operands: 44
39	Literal
40	Literal
41	Variable
42	Literal
43	Literal
44	ExprTuple	45, 46
45	Variable
46	Operation	operator: 47 operands: 48
47	Literal
48	ExprTuple	49, 50
49	Literal
50	Literal