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
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 = Mult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), Exp(e, Mult(two, pi, i, _phase, k)))
expr = ExprTuple(Conditional(sub_expr1, InSet(k, Interval(zero, subtract(two_pow_t, one)))), 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(\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\}, \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}\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: 20 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	27, 9
7	Operation	operator: 30 operands: 10
8	Operation	operator: 30 operands: 11
9	Operation	operator: 12 operands: 13
10	ExprTuple	15, 14
11	ExprTuple	15, 16
12	Literal
13	ExprTuple	17, 18
14	Operation	operator: 20 operands: 19
15	Literal
16	Operation	operator: 20 operands: 21
17	Literal
18	Operation	operator: 22 operands: 23
19	ExprTuple	34, 24, 25, 26, 28
20	Literal
21	ExprTuple	34, 24, 25, 26, 27
22	Literal
23	ExprTuple	28, 29
24	Literal
25	Literal
26	Literal
27	Variable
28	Operation	operator: 30 operands: 31
29	Operation	operator: 32 operand: 36
30	Literal
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	36
34	Literal
35	Variable
36	Literal