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, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Add, Exp, Mult, e, frac, i, one, pi, subtract, two
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(ScalarMult(frac(one, Exp(two, subtract(frac(Add(t, one), two), frac(t, two)))), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), ket1))))

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(\frac{1}{2^{\frac{t + 1}{2} - \frac{t}{2}}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \lvert 1 \rangle\right)\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Operation	operator: 13 operands: 2
2	ExprTuple	3, 4
3	Operation	operator: 40 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	44, 8
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 42 operands: 11
9	Operation	operator: 21 operand: 16
10	Operation	operator: 13 operands: 14
11	ExprTuple	45, 15
12	ExprTuple	16
13	Literal
14	ExprTuple	17, 18
15	Operation	operator: 38 operands: 19
16	Literal
17	Operation	operator: 42 operands: 20
18	Operation	operator: 21 operand: 44
19	ExprTuple	23, 24
20	ExprTuple	25, 26
21	Literal
22	ExprTuple	44
23	Operation	operator: 40 operands: 27
24	Operation	operator: 28 operand: 33
25	Literal
26	Operation	operator: 30 operands: 31
27	ExprTuple	32, 45
28	Literal
29	ExprTuple	33
30	Literal
31	ExprTuple	45, 34, 35, 36, 37
32	Operation	operator: 38 operands: 39
33	Operation	operator: 40 operands: 41
34	Literal
35	Literal
36	Literal
37	Operation	operator: 42 operands: 43
38	Literal
39	ExprTuple	46, 44
40	Literal
41	ExprTuple	46, 45
42	Literal
43	ExprTuple	45, 46
44	Literal
45	Literal
46	Variable