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
from proveit.logic import InSet
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Exp(e, Mult(two, pi, i, _phase, k))
sub_expr2 = Exp(e, Mult(two, pi, i, _phase, two_pow_t))
sub_expr3 = InSet(k, Interval(zero, subtract(two_pow_t, one)))
expr = ExprTuple(Lambda(k, Conditional(Mult(sub_expr1, sub_expr2), sub_expr3)), Lambda(k, Conditional(Mult(sub_expr2, sub_expr1), sub_expr3)))

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}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right.., k \mapsto \left\{\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \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: 33 body: 3
2	Lambda	parameter: 33 body: 5
3	Conditional	value: 6 condition: 8
4	ExprTuple	33
5	Conditional	value: 7 condition: 8
6	Operation	operator: 26 operands: 9
7	Operation	operator: 26 operands: 10
8	Operation	operator: 11 operands: 12
9	ExprTuple	14, 13
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	33, 15
13	Operation	operator: 36 operands: 16
14	Operation	operator: 36 operands: 17
15	Operation	operator: 18 operands: 19
16	ExprTuple	21, 20
17	ExprTuple	21, 22
18	Literal
19	ExprTuple	23, 24
20	Operation	operator: 26 operands: 25
21	Literal
22	Operation	operator: 26 operands: 27
23	Literal
24	Operation	operator: 28 operands: 29
25	ExprTuple	40, 30, 31, 32, 34
26	Literal
27	ExprTuple	40, 30, 31, 32, 33
28	Literal
29	ExprTuple	34, 35
30	Literal
31	Literal
32	Literal
33	Variable
34	Operation	operator: 36 operands: 37
35	Operation	operator: 38 operand: 42
36	Literal
37	ExprTuple	40, 41
38	Literal
39	ExprTuple	42
40	Literal
41	Variable
42	Literal