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, 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)))

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