# 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, e
from proveit.numbers import Add, Exp, Mult, Neg, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow_t

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Neg(e)
sub_expr2 = Mult(frac(one, Exp(two, one)), _two_pow_t)
sub_expr3 = Neg(sub_expr2)

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(\left(\frac{1}{2^{1}} \cdot 2^{t}\right) - 2\right) + \left(-\left(\frac{1}{2^{1}} \cdot 2^{t}\right) + 1 - e\right), \left(\frac{1}{2^{1}} \cdot 2^{t}\right) - 2 - \left(\frac{1}{2^{1}} \cdot 2^{t}\right) + 1 - e\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: 8
operands: 3
2Operationoperator: 8
operands: 4
3ExprTuple5, 6
4ExprTuple17, 10, 11, 31, 12
5Operationoperator: 8
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple17, 10
8Literal
9ExprTuple11, 31, 12
10Operationoperator: 15
operand: 30
11Operationoperator: 15
operand: 17
12Operationoperator: 15
operand: 18
13ExprTuple30
14ExprTuple17
15Literal
16ExprTuple18
17Operationoperator: 19
operands: 20
18Variable
19Literal
20ExprTuple21, 22
21Operationoperator: 23
operands: 24
22Operationoperator: 28
operands: 25
23Literal
24ExprTuple31, 26
25ExprTuple30, 27
26Operationoperator: 28
operands: 29
27Literal
28Literal
29ExprTuple30, 31
30Literal
31Literal