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, U
from proveit.linear_algebra import MatrixMult, ScalarMult
from proveit.logic import Equals, InSet
from proveit.numbers import Exp, Interval, IntervalCO, Mult, Real, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import var_ket_u
from proveit.physics.quantum.QPE import phase, two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(InSet(phase, Real), InSet(Mult(two_pow_t, phase), Interval(zero, subtract(two_pow_t, one))), Equals(MatrixMult(U, var_ket_u), ScalarMult(Exp(e, Mult(two, pi, i, phase)), var_ket_u)), InSet(phase, IntervalCO(zero, one)))

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(\varphi \in \mathbb{R}, \left(2^{t} \cdot \varphi\right) \in \{0~\ldotp \ldotp~2^{t} - 1\}, \left(U \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert u \rangle\right), \varphi \in \left[0,1\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, 3, 4
1	Operation	operator: 9 operands: 5
2	Operation	operator: 9 operands: 6
3	Operation	operator: 7 operands: 8
4	Operation	operator: 9 operands: 10
5	ExprTuple	49, 11
6	ExprTuple	12, 13
7	Literal
8	ExprTuple	14, 15
9	Literal
10	ExprTuple	49, 16
11	Literal
12	Operation	operator: 42 operands: 17
13	Operation	operator: 18 operands: 19
14	Operation	operator: 20 operands: 21
15	Operation	operator: 22 operands: 23
16	Operation	operator: 24 operands: 25
17	ExprTuple	34, 49
18	Literal
19	ExprTuple	30, 26
20	Literal
21	ExprTuple	27, 29
22	Literal
23	ExprTuple	28, 29
24	Literal
25	ExprTuple	30, 45
26	Operation	operator: 31 operands: 32
27	Variable
28	Operation	operator: 38 operands: 33
29	Variable
30	Literal
31	Literal
32	ExprTuple	34, 35
33	ExprTuple	36, 37
34	Operation	operator: 38 operands: 39
35	Operation	operator: 40 operand: 45
36	Literal
37	Operation	operator: 42 operands: 43
38	Literal
39	ExprTuple	46, 44
40	Literal
41	ExprTuple	45
42	Literal
43	ExprTuple	46, 47, 48, 49
44	Variable
45	Literal
46	Literal
47	Literal
48	Literal
49	Variable