# from the theory of proveit.physics.quantum.QPE¶

In [1]:
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.
# import Expression classes needed to build the expression
from proveit import ExprTuple
from proveit.numbers import Add, Exp, Mult, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one, _two_pow_t

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Add(subtract(_two_pow__t_minus_one, two), one), subtract(Mult(frac(one, Exp(two, one)), _two_pow_t), one))

expr:
In [3]:
# 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

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(2^{t - 1} - 2\right) + 1, \left(\frac{1}{2^{1}} \cdot 2^{t}\right) - 1\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1, 2
1Operationoperator: 21
operands: 3
2Operationoperator: 21
operands: 4
3ExprTuple5, 30
4ExprTuple6, 26
5Operationoperator: 21
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 11
8Literal
9ExprTuple12, 13
10Operationoperator: 23
operands: 14
11Operationoperator: 28
operand: 27
12Operationoperator: 16
operands: 17
13Operationoperator: 23
operands: 18
14ExprTuple27, 19
15ExprTuple27
16Literal
17ExprTuple30, 20
18ExprTuple27, 25
19Operationoperator: 21
operands: 22
20Operationoperator: 23
operands: 24
21Literal
22ExprTuple25, 26
23Literal
24ExprTuple27, 30
25Literal
26Operationoperator: 28
operand: 30
27Literal
28Literal
29ExprTuple30
30Literal